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dividing by 10 , a lot like multiplying by 10 , creates a pattern with numbers . so let 's dig in and look at dividing by 10 and look at happens when we divide by 10 and see if we can figure out that pattern and maybe even how it relates to the pattern for multiplying by 10 . let 's take a fairly simple one to start .... | dividing by 10 , a lot like multiplying by 10 , creates a pattern with numbers . so let 's dig in and look at dividing by 10 and look at happens when we divide by 10 and see if we can figure out that pattern and maybe even how it relates to the pattern for multiplying by 10 . let 's take a fairly simple one to start . | what is the pattern of dividing by ten ? |
dividing by 10 , a lot like multiplying by 10 , creates a pattern with numbers . so let 's dig in and look at dividing by 10 and look at happens when we divide by 10 and see if we can figure out that pattern and maybe even how it relates to the pattern for multiplying by 10 . let 's take a fairly simple one to start .... | remember , in another one , something like 13 times 10 , our product , our solution is a 13 , the original number , with a zero added to the end . so in multiplication , when we multiply by 10 , we add a zero to our whole number at the end , and when we divide , we do the opposite by 10 , we take off a zero from the en... | why are decimals involved , are n't we multiply and divising ? |
: psychologists and sociologists study human behavior . as they study behavior , they 're often asked , what is normal ? who decides what behavior is normal ? how do we determine if a person 's behavior is strange , or even criminal ? the individuals who seek to understand those questions and define their answers actu... | there 's no actual punishment or strong issue with refusing to help a person whose dropped an item in a grocery store . it just might be seen as rude , so those are folkways . now , let 's talk about mores . | i know this might be a difficult question to contemplate on , but is there a real reason why incest should be illegal ? |
: psychologists and sociologists study human behavior . as they study behavior , they 're often asked , what is normal ? who decides what behavior is normal ? how do we determine if a person 's behavior is strange , or even criminal ? the individuals who seek to understand those questions and define their answers actu... | they 're based in a deep understanding of right and wrong and the violation of a taboo results in consequences that are far more extreme than more . now , it is a norm to not engage in taboos , and if a taboo is committed , it is considered very immoral behavior . taboos are often punishable by law and taboos also usua... | is homosexuality considered a more , folkway , or taboo ? |
i 've talked a lot about how our change in internal energy of a system can be due to some heat being added to the system , or some work being added to the system , or being done to the system . and i 'm going to write it again the other way , just because you see it both ways . you could say that the change in internal... | i 've talked a lot about how our change in internal energy of a system can be due to some heat being added to the system , or some work being added to the system , or being done to the system . and i 'm going to write it again the other way , just because you see it both ways . | what is an adiabatic process and how do you know if the system is adiabatic ? |
i 've talked a lot about how our change in internal energy of a system can be due to some heat being added to the system , or some work being added to the system , or being done to the system . and i 'm going to write it again the other way , just because you see it both ways . you could say that the change in internal... | we can write work done by our system . work done is equal to pressure times our change in volume . now this has a very interesting repercussion here . | why change in volume is not infinitesimal but change in pressure is ? |
i 've talked a lot about how our change in internal energy of a system can be due to some heat being added to the system , or some work being added to the system , or being done to the system . and i 'm going to write it again the other way , just because you see it both ways . you could say that the change in internal... | so we can write work now in terms of things that we know . we can write work done by our system . work done is equal to pressure times our change in volume . | is pv work the only kind of work a system can do ? |
i 've talked a lot about how our change in internal energy of a system can be due to some heat being added to the system , or some work being added to the system , or being done to the system . and i 'm going to write it again the other way , just because you see it both ways . you could say that the change in internal... | so what is the force that it pushed it up ? well , the force , we know its pressure , the pressure 's force per area . so if we want to know the force , we have to multiply pressure times area . | when sal defines the pressure and force , why does he assume that the force applied on the ceiling of the piston is constant ? |
i 've talked a lot about how our change in internal energy of a system can be due to some heat being added to the system , or some work being added to the system , or being done to the system . and i 'm going to write it again the other way , just because you see it both ways . you could say that the change in internal... | so what is the force that it pushed it up ? well , the force , we know its pressure , the pressure 's force per area . so if we want to know the force , we have to multiply pressure times area . | as the volume increases by the force pushing the ceiling a distance `` x '' , should n't the pressure decrease ? |
i 've talked a lot about how our change in internal energy of a system can be due to some heat being added to the system , or some work being added to the system , or being done to the system . and i 'm going to write it again the other way , just because you see it both ways . you could say that the change in internal... | in this case , the system is pushing these marbles , or these pieces of sand up . it 's doing work . if we were doing it the other way , if we were adding the sand , and we were pushing down on our little canister , we would be doing work to the system . | why are heat and work not state functions ? |
i 've talked a lot about how our change in internal energy of a system can be due to some heat being added to the system , or some work being added to the system , or being done to the system . and i 'm going to write it again the other way , just because you see it both ways . you could say that the change in internal... | i 've talked a lot about how our change in internal energy of a system can be due to some heat being added to the system , or some work being added to the system , or being done to the system . and i 'm going to write it again the other way , just because you see it both ways . | why are the conventions different ? |
i 've talked a lot about how our change in internal energy of a system can be due to some heat being added to the system , or some work being added to the system , or being done to the system . and i 'm going to write it again the other way , just because you see it both ways . you could say that the change in internal... | we can write work done by our system . work done is equal to pressure times our change in volume . now this has a very interesting repercussion here . | why not external pressure times change in volume because the gas has managed to do work against the external pressure conditions ? |
i 've talked a lot about how our change in internal energy of a system can be due to some heat being added to the system , or some work being added to the system , or being done to the system . and i 'm going to write it again the other way , just because you see it both ways . you could say that the change in internal... | we can write work done by our system . work done is equal to pressure times our change in volume . now this has a very interesting repercussion here . | if a container containing a specific amount of an ideal gas ( no heat transmission ) expand in volume , how will the internal pressure an tenperature change in respond to the change in volume ? |
i 've talked a lot about how our change in internal energy of a system can be due to some heat being added to the system , or some work being added to the system , or being done to the system . and i 'm going to write it again the other way , just because you see it both ways . you could say that the change in internal... | now this has a very interesting repercussion here . so we could -- actually many -- we can rewrite our internal energy formulas . so , for example , we can write internal change and internal energy is now equal to heat added to the system , plus the work -- let me say minus the work done by the system . well what is th... | how can you write change in internal energy in 'q ' form ? |
i 've talked a lot about how our change in internal energy of a system can be due to some heat being added to the system , or some work being added to the system , or being done to the system . and i 'm going to write it again the other way , just because you see it both ways . you could say that the change in internal... | so we can write work now in terms of things that we know . we can write work done by our system . work done is equal to pressure times our change in volume . | can someone give me a summary of what happens to all the macrostates when the system does work/has work done on it ? |
i 've talked a lot about how our change in internal energy of a system can be due to some heat being added to the system , or some work being added to the system , or being done to the system . and i 'm going to write it again the other way , just because you see it both ways . you could say that the change in internal... | so what is the force that it pushed it up ? well , the force , we know its pressure , the pressure 's force per area . so if we want to know the force , we have to multiply pressure times area . | in a equilibrium cuboid system , if you say that all the walls are experiencing same pressure does that indicate that the wall with larger area is experiencing more force ... .how ? |
i 've talked a lot about how our change in internal energy of a system can be due to some heat being added to the system , or some work being added to the system , or being done to the system . and i 'm going to write it again the other way , just because you see it both ways . you could say that the change in internal... | i 've talked a lot about how our change in internal energy of a system can be due to some heat being added to the system , or some work being added to the system , or being done to the system . and i 'm going to write it again the other way , just because you see it both ways . | does an adiabatic process take place in an isolated system or a closed system ? |
i 've talked a lot about how our change in internal energy of a system can be due to some heat being added to the system , or some work being added to the system , or being done to the system . and i 'm going to write it again the other way , just because you see it both ways . you could say that the change in internal... | now what 's the distance ? the distance is this x over here . the distance is -- i 'll do it in blue -- it 's this change right here . | and also , does sa x h = v always true ? |
i 've talked a lot about how our change in internal energy of a system can be due to some heat being added to the system , or some work being added to the system , or being done to the system . and i 'm going to write it again the other way , just because you see it both ways . you could say that the change in internal... | we know the pressure that 's being exerted on the piston , at least at this point in time . and what 's pressure ? pressure is equal to force per area . remember , this piston , you 're just seeing it from the side , but it 's a kind of a flat plate or a flat ceiling on top of this thing . | is the internal pressure is equal to external atmospheric pressure ? |
i 've talked a lot about how our change in internal energy of a system can be due to some heat being added to the system , or some work being added to the system , or being done to the system . and i 'm going to write it again the other way , just because you see it both ways . you could say that the change in internal... | i 've talked a lot about how our change in internal energy of a system can be due to some heat being added to the system , or some work being added to the system , or being done to the system . and i 'm going to write it again the other way , just because you see it both ways . | are the examples sal mentioned account for gravity ? |
i 've talked a lot about how our change in internal energy of a system can be due to some heat being added to the system , or some work being added to the system , or being done to the system . and i 'm going to write it again the other way , just because you see it both ways . you could say that the change in internal... | so i 'm going to leave you there in this video . in the next video , we 're going to relate this , this new way of writing our internal energy formula , and we 're going to relate it to the pv diagram . | so can q-pv and q+pv be used interchangeably like q-w and q+w as long as you understand the context ? |
i 've talked a lot about how our change in internal energy of a system can be due to some heat being added to the system , or some work being added to the system , or being done to the system . and i 'm going to write it again the other way , just because you see it both ways . you could say that the change in internal... | now this has a very interesting repercussion here . so we could -- actually many -- we can rewrite our internal energy formulas . so , for example , we can write internal change and internal energy is now equal to heat added to the system , plus the work -- let me say minus the work done by the system . well what is th... | what is the exact formula for change in internal energy ? |
i 've talked a lot about how our change in internal energy of a system can be due to some heat being added to the system , or some work being added to the system , or being done to the system . and i 'm going to write it again the other way , just because you see it both ways . you could say that the change in internal... | and how is work done , or done by , or done to a system ? the heat , i think , is fairly intuitive . if i have a -- and we 'll be a little bit more precise in the future of this , but i just want to give you the sense of what we 're talking about -- if i have some system here , some particles in some type of a canister... | why does a manual air-pump heat up while we are pumping air from it ? |
i 've talked a lot about how our change in internal energy of a system can be due to some heat being added to the system , or some work being added to the system , or being done to the system . and i 'm going to write it again the other way , just because you see it both ways . you could say that the change in internal... | and how is work done , or done by , or done to a system ? the heat , i think , is fairly intuitive . if i have a -- and we 'll be a little bit more precise in the future of this , but i just want to give you the sense of what we 're talking about -- if i have some system here , some particles in some type of a canister... | temperature and heat are two different terms ? |
i 've talked a lot about how our change in internal energy of a system can be due to some heat being added to the system , or some work being added to the system , or being done to the system . and i 'm going to write it again the other way , just because you see it both ways . you could say that the change in internal... | and how is work done , or done by , or done to a system ? the heat , i think , is fairly intuitive . if i have a -- and we 'll be a little bit more precise in the future of this , but i just want to give you the sense of what we 're talking about -- if i have some system here , some particles in some type of a canister... | is the unit of heat is joules ? |
i 've talked a lot about how our change in internal energy of a system can be due to some heat being added to the system , or some work being added to the system , or being done to the system . and i 'm going to write it again the other way , just because you see it both ways . you could say that the change in internal... | we can write work done by our system . work done is equal to pressure times our change in volume . now this has a very interesting repercussion here . | during the change in volume ; or if looking at the situation quasi-statically , is n't both the change in pressure and volume too negligible to be considered ? |
i 've talked a lot about how our change in internal energy of a system can be due to some heat being added to the system , or some work being added to the system , or being done to the system . and i 'm going to write it again the other way , just because you see it both ways . you could say that the change in internal... | we have some surface area . surface area times height is volume . so this right here , this term right here , is a change in volume . | why the value of co-efficient of volume expansion of same material is thrice the value of the co-efficient of linear expansion ? |
i 've talked a lot about how our change in internal energy of a system can be due to some heat being added to the system , or some work being added to the system , or being done to the system . and i 'm going to write it again the other way , just because you see it both ways . you could say that the change in internal... | so we 're essentially saying the area of this little ceiling to this container right there , you know , it could be , i could draw with some depth , but i think you know what i 'm talking about . it has some area . it 's probably the same area as the base of the container . so we could say that the force being applied ... | sal says that the area of the piston = area of the base of the container but dose n't the base of container have walls on it 's sides ? |
i 've talked a lot about how our change in internal energy of a system can be due to some heat being added to the system , or some work being added to the system , or being done to the system . and i 'm going to write it again the other way , just because you see it both ways . you could say that the change in internal... | so if we go back to our little formula , that internal energy is heat minus the work done by a system , so done by , then we can write this as , this is equal to the heat added to the system minus this quantity , the pressure of the system , times the change in volume . and it 's interesting , if the volume is increasi... | keeping in mind that pressure inside the system is also decreasing with increasing volume ? |
i 've talked a lot about how our change in internal energy of a system can be due to some heat being added to the system , or some work being added to the system , or being done to the system . and i 'm going to write it again the other way , just because you see it both ways . you could say that the change in internal... | now this has a very interesting repercussion here . so we could -- actually many -- we can rewrite our internal energy formulas . so , for example , we can write internal change and internal energy is now equal to heat added to the system , plus the work -- let me say minus the work done by the system . | in isothermal expansion , why internal energy depends only on temperature ? |
i 've talked a lot about how our change in internal energy of a system can be due to some heat being added to the system , or some work being added to the system , or being done to the system . and i 'm going to write it again the other way , just because you see it both ways . you could say that the change in internal... | i 've talked a lot about how our change in internal energy of a system can be due to some heat being added to the system , or some work being added to the system , or being done to the system . and i 'm going to write it again the other way , just because you see it both ways . | why wrev is greater than wirr ? |
i 've talked a lot about how our change in internal energy of a system can be due to some heat being added to the system , or some work being added to the system , or being done to the system . and i 'm going to write it again the other way , just because you see it both ways . you could say that the change in internal... | and then we moved it some distance x . now , we could rearrange this . we could say that the work is equal to our pressure times our area , times x . | could someone tell me when to use -p and +p ? |
i 've talked a lot about how our change in internal energy of a system can be due to some heat being added to the system , or some work being added to the system , or being done to the system . and i 'm going to write it again the other way , just because you see it both ways . you could say that the change in internal... | when you look at it with a little bit of depth , you see the rectangle also did n't get taller . we have some surface area . surface area times height is volume . | is surface area a macrostate variable of a system ? |
i 've talked a lot about how our change in internal energy of a system can be due to some heat being added to the system , or some work being added to the system , or being done to the system . and i 'm going to write it again the other way , just because you see it both ways . you could say that the change in internal... | we have some surface area . surface area times height is volume . so this right here , this term right here , is a change in volume . | in the case of when volume is falling , do we use deltau = q + p * deltav ? |
i 've talked a lot about how our change in internal energy of a system can be due to some heat being added to the system , or some work being added to the system , or being done to the system . and i 'm going to write it again the other way , just because you see it both ways . you could say that the change in internal... | heat is changing the macrostate of our systems . this system is going to lose temperature . this system 's going to gain temperature . | on the example with the heat transfer , why does the second system lose temperature ? |
i 've talked a lot about how our change in internal energy of a system can be due to some heat being added to the system , or some work being added to the system , or being done to the system . and i 'm going to write it again the other way , just because you see it both ways . you could say that the change in internal... | heat is changing the macrostate of our systems . this system is going to lose temperature . this system 's going to gain temperature . | i understand why the first system gain temperature , but why does the second system lose temperature ? |
i 've talked a lot about how our change in internal energy of a system can be due to some heat being added to the system , or some work being added to the system , or being done to the system . and i 'm going to write it again the other way , just because you see it both ways . you could say that the change in internal... | and let 's just think about that . so work , according to the definitions that you learned in first-year physics , and when you 're using classical or dealing with classical mechanics , you learn that work is equal to force times distance . so if i 'm claiming that when this piston moved up a little bit , when i remove... | could we figure out the work done by the gas by calculating the opposite force which the removed pebbles were exerting on the gas and then using that value in the work=force x distance formula ? |
i 've talked a lot about how our change in internal energy of a system can be due to some heat being added to the system , or some work being added to the system , or being done to the system . and i 'm going to write it again the other way , just because you see it both ways . you could say that the change in internal... | heat is changing the macrostate of our systems . this system is going to lose temperature . this system 's going to gain temperature . | if a system is heated and its temperature increased wo n't it expand and increase in volume by charles ' law , hence performing work ? |
i 've talked a lot about how our change in internal energy of a system can be due to some heat being added to the system , or some work being added to the system , or being done to the system . and i 'm going to write it again the other way , just because you see it both ways . you could say that the change in internal... | so i have my container . there you go . it 's got a little movable ceiling to it . | how would you go about solving for average increase in the velocity of the molecules ? |
i 've talked a lot about how our change in internal energy of a system can be due to some heat being added to the system , or some work being added to the system , or being done to the system . and i 'm going to write it again the other way , just because you see it both ways . you could say that the change in internal... | and how is work done , or done by , or done to a system ? the heat , i think , is fairly intuitive . if i have a -- and we 'll be a little bit more precise in the future of this , but i just want to give you the sense of what we 're talking about -- if i have some system here , some particles in some type of a canister... | i 'm confused so what is the difference between heat and temperature , you 're basically showing that they are the same ? |
i 've talked a lot about how our change in internal energy of a system can be due to some heat being added to the system , or some work being added to the system , or being done to the system . and i 'm going to write it again the other way , just because you see it both ways . you could say that the change in internal... | so there 's two questions that might naturally spring up in your head . one is , how is heat added to or taken away from a system ? and how is work done , or done by , or done to a system ? the heat , i think , is fairly intuitive . | is the force done by the system equals to weight of the 'marble ' taken away itself ? |
i 've talked a lot about how our change in internal energy of a system can be due to some heat being added to the system , or some work being added to the system , or being done to the system . and i 'm going to write it again the other way , just because you see it both ways . you could say that the change in internal... | you know i could blow it up a little bit . it moved it some -- i did n't draw it too big here -- some x , some distance x . so this change , it moved it up some distance x there , right ? so what is the force that it pushed it up ? well , the force , we know its pressure , the pressure 's force per area . so if we want... | why did you put force=p*a*x ? |
i 've talked a lot about how our change in internal energy of a system can be due to some heat being added to the system , or some work being added to the system , or being done to the system . and i 'm going to write it again the other way , just because you see it both ways . you could say that the change in internal... | one is , how is heat added to or taken away from a system ? and how is work done , or done by , or done to a system ? the heat , i think , is fairly intuitive . | force is just p*a pax defines the work done , no ? |
i 've talked a lot about how our change in internal energy of a system can be due to some heat being added to the system , or some work being added to the system , or being done to the system . and i 'm going to write it again the other way , just because you see it both ways . you could say that the change in internal... | what 's this area , this area right here , times x ? well that 's going to be our change in volume , right ? this area times some height is some volume . | near the end when he mentions the `` change in volume , '' why ca n't it just be v ? |
i 've talked a lot about how our change in internal energy of a system can be due to some heat being added to the system , or some work being added to the system , or being done to the system . and i 'm going to write it again the other way , just because you see it both ways . you could say that the change in internal... | so there 's two questions that might naturally spring up in your head . one is , how is heat added to or taken away from a system ? and how is work done , or done by , or done to a system ? | if del u = q-pdel v how can the heat be added to the system as sal says ? |
i 've talked a lot about how our change in internal energy of a system can be due to some heat being added to the system , or some work being added to the system , or being done to the system . and i 'm going to write it again the other way , just because you see it both ways . you could say that the change in internal... | we have some surface area . surface area times height is volume . so this right here , this term right here , is a change in volume . | how do you calculate volume related questions in first law of thermodynamics , is there a formula ? |
i 've talked a lot about how our change in internal energy of a system can be due to some heat being added to the system , or some work being added to the system , or being done to the system . and i 'm going to write it again the other way , just because you see it both ways . you could say that the change in internal... | in this case , the system is pushing these marbles , or these pieces of sand up . it 's doing work . if we were doing it the other way , if we were adding the sand , and we were pushing down on our little canister , we would be doing work to the system . | so work and heat are the same thing at the atomic level ? |
i 've talked a lot about how our change in internal energy of a system can be due to some heat being added to the system , or some work being added to the system , or being done to the system . and i 'm going to write it again the other way , just because you see it both ways . you could say that the change in internal... | and how is work done , or done by , or done to a system ? the heat , i think , is fairly intuitive . if i have a -- and we 'll be a little bit more precise in the future of this , but i just want to give you the sense of what we 're talking about -- if i have some system here , some particles in some type of a canister... | if we consider that there 's a little displacement of particles , then we can think of heat as work , w = f*d. so why do we make a distinction between the two ? |
i 've talked a lot about how our change in internal energy of a system can be due to some heat being added to the system , or some work being added to the system , or being done to the system . and i 'm going to write it again the other way , just because you see it both ways . you could say that the change in internal... | one is , how is heat added to or taken away from a system ? and how is work done , or done by , or done to a system ? the heat , i think , is fairly intuitive . | when the original formula of work done by the system is deltau = q - w ? |
- what i hope to do in this video is get even more algebraically familiar with the lorentz transformation , so that we can recognize it in its different forms and start to build our intuition for how it behaves . so let 's just write down the lorentz transformation , or at least the way that i like to write it . so let... | we saw how the angles in the minkowski diagram , how those were symmetrical , the angles between the regular , or the unprimed axes , and the primed axes . and so what i do n't like about this is you no longer see the symmetry , while you did see it the first way that i wrote it . and frankly i find this harder to reme... | why is it so important to see the symmetry ? |
- what i hope to do in this video is get even more algebraically familiar with the lorentz transformation , so that we can recognize it in its different forms and start to build our intuition for how it behaves . so let 's just write down the lorentz transformation , or at least the way that i like to write it . so let... | start evaluating this , evaluate this for v 's in our everyday life , and then see what happens when v starts to approach .8 times the speed of light . .9 c , .99 c , think about what happens to the lorentz factor . and hopefully you 'll get an appreciation for how this whole thing behaves . | if v approaches c would the lorentz factor equal infinite ? |
- what i hope to do in this video is get even more algebraically familiar with the lorentz transformation , so that we can recognize it in its different forms and start to build our intuition for how it behaves . so let 's just write down the lorentz transformation , or at least the way that i like to write it . so let... | so vx , v times x over c-squared . and this is actually a more typical way , both of these , of seeing the lorentz transformation . the reason why i do n't like this form as much , even though this does have the neat , kind of , when you look at it , it looks like you 're just scaling up the galilean transformation , i... | must a symmetry be the invariance of a particular laws form under some transformation ( a change of something the law is described interms of , or can it be the invariance of something else ? |
- what i hope to do in this video is get even more algebraically familiar with the lorentz transformation , so that we can recognize it in its different forms and start to build our intuition for how it behaves . so let 's just write down the lorentz transformation , or at least the way that i like to write it . so let... | so let 's also divide both sides by c , so you divide by c there , and you can divide by c there , and you can divide by c there , those c 's cancel , those c 's cancel , and so we 're left with t-prime is equal to the lorentz factor , times t times t minus , now you 're going to get v times x , and you 're going to di... | in what way is the function y = [ 1/sqrt ( 1-v^2/c^2 ) ] in the x scaling of the galilean transformation seen as analogous to the projection operator functions cos q evaluated at q=tan-1 ( v/c ) and the yv function analogous to the circular function sin , for projecting the x and t coordinates onto the x ' tilted ( at ... |
- what i hope to do in this video is get even more algebraically familiar with the lorentz transformation , so that we can recognize it in its different forms and start to build our intuition for how it behaves . so let 's just write down the lorentz transformation , or at least the way that i like to write it . so let... | we saw how the angles in the minkowski diagram , how those were symmetrical , the angles between the regular , or the unprimed axes , and the primed axes . and so what i do n't like about this is you no longer see the symmetry , while you did see it the first way that i wrote it . and frankly i find this harder to reme... | how do we see y as a projection function analogous to the way we see cos as a projection function ? |
- what i hope to do in this video is get even more algebraically familiar with the lorentz transformation , so that we can recognize it in its different forms and start to build our intuition for how it behaves . so let 's just write down the lorentz transformation , or at least the way that i like to write it . so let... | so let 's also divide both sides by c , so you divide by c there , and you can divide by c there , and you can divide by c there , those c 's cancel , those c 's cancel , and so we 're left with t-prime is equal to the lorentz factor , times t times t minus , now you 're going to get v times x , and you 're going to di... | why do n't we get ( y/c ) [ t- ( v/c^2 ) x ] instead of y [ t- ( v^2/x^2 ) ] ? |
- what i hope to do in this video is get even more algebraically familiar with the lorentz transformation , so that we can recognize it in its different forms and start to build our intuition for how it behaves . so let 's just write down the lorentz transformation , or at least the way that i like to write it . so let... | i find it easier to remember . i find it easier to remember because it has this nice , beautiful symmetry to it . when i 'm trying to solve for x-prime , it 's x minus beta times ct . | but what is the law in the spacetime that is invariant , and under what transformations does this symmetry ( invariance ) hold ( what change is this symmetry applicable for ) ? |
- what i hope to do in this video is get even more algebraically familiar with the lorentz transformation , so that we can recognize it in its different forms and start to build our intuition for how it behaves . so let 's just write down the lorentz transformation , or at least the way that i like to write it . so let... | so vx , v times x over c-squared . and this is actually a more typical way , both of these , of seeing the lorentz transformation . the reason why i do n't like this form as much , even though this does have the neat , kind of , when you look at it , it looks like you 're just scaling up the galilean transformation , i... | my question : would it be accurate to say the lorentz transformation is just a more informed and accurate method of galilean transformations because we 're following quantum rules ? |
- what i hope to do in this video is get even more algebraically familiar with the lorentz transformation , so that we can recognize it in its different forms and start to build our intuition for how it behaves . so let 's just write down the lorentz transformation , or at least the way that i like to write it . so let... | when i 'm solving for ct-prime , it 's ct minus beta times x . and in both cases , i 'm scaling by the lorentz factor . well let 's manipulate this a little bit , just to understand a little better , and reconcile with what you might see with other sources , including , say , your textbook . | what is a scaling factor ? |
- what i hope to do in this video is get even more algebraically familiar with the lorentz transformation , so that we can recognize it in its different forms and start to build our intuition for how it behaves . so let 's just write down the lorentz transformation , or at least the way that i like to write it . so let... | if it was just x minus vt , that was just our intuition about our everyday life , but newtonian physics would actually tell us , and so when you view it in this form , you really think , okay , you 're just going to scale that by this lorentz transformation , which has this interesting behavior that if v is much , much... | why does the lorentz scaling factor put into the galilean transformations give us the results that this amended galilean transformation will give a constant speed of light for both frames when without this scaling factor the galilean tranformations would predict different values for the speed of light in each frame ? |
triangle sam , s-a-m , and this is one over here , s-a-m , is rotated 270 degrees , about the point four comma negative two . so , this is four comma negative two right over here . draw the image of this rotation using the interactive graph . we have this little interactive graph tool where we can draw points or if we... | so , this is four comma negative two right over here . draw the image of this rotation using the interactive graph . we have this little interactive graph tool where we can draw points or if we wan na put them in the trash we can put them there . | can we rotate it by using the patterns of the rotations and thinking of the point of rotation as the origin ? |
triangle sam , s-a-m , and this is one over here , s-a-m , is rotated 270 degrees , about the point four comma negative two . so , this is four comma negative two right over here . draw the image of this rotation using the interactive graph . we have this little interactive graph tool where we can draw points or if we... | now we have to go back onto the exercise and put it in . so , let 's remember these points . we have the point eight comma five . | is there a formula that we can use for arbitrary points ? |
triangle sam , s-a-m , and this is one over here , s-a-m , is rotated 270 degrees , about the point four comma negative two . so , this is four comma negative two right over here . draw the image of this rotation using the interactive graph . we have this little interactive graph tool where we can draw points or if we... | so , we have the point one comma five and now i just have to finish it by going to this point again and we 're all done . we 've rotated it by 270 degrees which is equivalent to a negative 90 degree rotation . we can check that we indeed got it right . | how do you find the center of rotation when you have the original figure and the rotated figure when it is not the origin ? |
triangle sam , s-a-m , and this is one over here , s-a-m , is rotated 270 degrees , about the point four comma negative two . so , this is four comma negative two right over here . draw the image of this rotation using the interactive graph . we have this little interactive graph tool where we can draw points or if we... | so , this is four comma negative two right over here . draw the image of this rotation using the interactive graph . we have this little interactive graph tool where we can draw points or if we wan na put them in the trash we can put them there . | can we rotate it by using the patterns of the rotations and thinking of the point of rotation as the origin ? |
triangle sam , s-a-m , and this is one over here , s-a-m , is rotated 270 degrees , about the point four comma negative two . so , this is four comma negative two right over here . draw the image of this rotation using the interactive graph . we have this little interactive graph tool where we can draw points or if we... | triangle sam , s-a-m , and this is one over here , s-a-m , is rotated 270 degrees , about the point four comma negative two . so , this is four comma negative two right over here . | do we have to draw a triangle to each point or we can find out the whole rotated shape by finding one point of a rotated shape ? |
triangle sam , s-a-m , and this is one over here , s-a-m , is rotated 270 degrees , about the point four comma negative two . so , this is four comma negative two right over here . draw the image of this rotation using the interactive graph . we have this little interactive graph tool where we can draw points or if we... | triangle sam , s-a-m , and this is one over here , s-a-m , is rotated 270 degrees , about the point four comma negative two . so , this is four comma negative two right over here . | how can you copy the white board from the website to your scratchpad ? |
triangle sam , s-a-m , and this is one over here , s-a-m , is rotated 270 degrees , about the point four comma negative two . so , this is four comma negative two right over here . draw the image of this rotation using the interactive graph . we have this little interactive graph tool where we can draw points or if we... | so , this top side , this top side right over here . if i were to rotate it , if i were to rotate it negative 90 degrees , 90 degrees in the clockwise direction , where does that put us ? well , once again it 's gon na put us straight up and down and this length is it goes from x equals negative three to x equals four ... | i have the points ( -4 , -2 ) ( -1,3 ) ( -6,2 ) and i have to rotate it on the point ( 1 , -2 ) 90 degrees clockwise and counter clockwise can you help ? |
triangle sam , s-a-m , and this is one over here , s-a-m , is rotated 270 degrees , about the point four comma negative two . so , this is four comma negative two right over here . draw the image of this rotation using the interactive graph . we have this little interactive graph tool where we can draw points or if we... | i could , i could draw this . the hypotenuse we know is gon na go from here to , from point a to our center of origin . and i could draw a right triangle that 's up here like this or i could draw a right triangle that is down here like this . | is there a type of formula or structure that can help me to create a formula without the point being the origin ? |
triangle sam , s-a-m , and this is one over here , s-a-m , is rotated 270 degrees , about the point four comma negative two . so , this is four comma negative two right over here . draw the image of this rotation using the interactive graph . we have this little interactive graph tool where we can draw points or if we... | so , this top side , this top side right over here . if i were to rotate it , if i were to rotate it negative 90 degrees , 90 degrees in the clockwise direction , where does that put us ? well , once again it 's gon na put us straight up and down and this length is it goes from x equals negative three to x equals four ... | i feel dumb ... but how do you rotate a square 90 degrees around its center ? |
triangle sam , s-a-m , and this is one over here , s-a-m , is rotated 270 degrees , about the point four comma negative two . so , this is four comma negative two right over here . draw the image of this rotation using the interactive graph . we have this little interactive graph tool where we can draw points or if we... | let 's do that . so , hypotenuse , we 'll connect point s to our center of rotation , and i can do this several ways . let me think about the best way to do it . | how do you find the center of a rotation ? |
triangle sam , s-a-m , and this is one over here , s-a-m , is rotated 270 degrees , about the point four comma negative two . so , this is four comma negative two right over here . draw the image of this rotation using the interactive graph . we have this little interactive graph tool where we can draw points or if we... | now , we just have to do this for point s and then we have the three points for our image . so , point s , once again we can construct a right triangle . let 's do that . | how would you use the `` right triangle method '' if the point of rotation was above or below a point to be rotated ? |
we 're on problem 55 . at a certain picnic each of the guests was served either a single scoop or a double scoop of ice cream . how many of the guests were served a double scoop of ice cream ? so let 's say that d is the number of guests that were served double scoop and that 's what we 're trying to figure out . so wh... | if x is 1 , 1 is equal to 1 squared . x ca n't be negative 1 . negative 1 is not equal to negative 1 squared . | 55. why ca n't i use x for single scoop and 2x for double scoop ? |
we 're on problem 55 . at a certain picnic each of the guests was served either a single scoop or a double scoop of ice cream . how many of the guests were served a double scoop of ice cream ? so let 's say that d is the number of guests that were served double scoop and that 's what we 're trying to figure out . so wh... | if x is 1 , 1 is equal to 1 squared . x ca n't be negative 1 . negative 1 is not equal to negative 1 squared . | why ca n't i used s+2s to denote single scoop and 2s to denote double scoop ? |
draw a circle and label the radius , diameter , center and the circumference . let me draw a circle , it wo n't be that well drawn of a circle but i think you get the idea so that is my circle . i 'm going to label the center..over here . so i 'll do the center i 'll call it 'c ' . so that is my center ... .and i 'll d... | and i could have drawn it other ways , i could have drawn it like this that would be another diameter it would have the exact same length and finally , we have to think about the circumference , and the circumference is really just how far you have to go to go around the circle or if you put a string on that circle , h... | is n't the circumference basically a perimeter ? |
draw a circle and label the radius , diameter , center and the circumference . let me draw a circle , it wo n't be that well drawn of a circle but i think you get the idea so that is my circle . i 'm going to label the center..over here . so i 'll do the center i 'll call it 'c ' . so that is my center ... .and i 'll d... | draw a circle and label the radius , diameter , center and the circumference . let me draw a circle , it wo n't be that well drawn of a circle but i think you get the idea so that is my circle . i 'm going to label the center..over here . | is the circumference of a circle like the perimeter of the circle ? |
draw a circle and label the radius , diameter , center and the circumference . let me draw a circle , it wo n't be that well drawn of a circle but i think you get the idea so that is my circle . i 'm going to label the center..over here . so i 'll do the center i 'll call it 'c ' . so that is my center ... .and i 'll d... | draw a circle and label the radius , diameter , center and the circumference . let me draw a circle , it wo n't be that well drawn of a circle but i think you get the idea so that is my circle . | what does the 'd ' stand for ? |
draw a circle and label the radius , diameter , center and the circumference . let me draw a circle , it wo n't be that well drawn of a circle but i think you get the idea so that is my circle . i 'm going to label the center..over here . so i 'll do the center i 'll call it 'c ' . so that is my center ... .and i 'll d... | so for example this would be a diameter.. that would be a diameter , you have one radii and another radii all on one line going from one side of the circle to another going through the center . so that is a diameter ! ^_^ ... ... .. that is a diameter . | how can you find the length between the radious and the diameter ? |
draw a circle and label the radius , diameter , center and the circumference . let me draw a circle , it wo n't be that well drawn of a circle but i think you get the idea so that is my circle . i 'm going to label the center..over here . so i 'll do the center i 'll call it 'c ' . so that is my center ... .and i 'll d... | draw a circle and label the radius , diameter , center and the circumference . let me draw a circle , it wo n't be that well drawn of a circle but i think you get the idea so that is my circle . | are there other types of lines with specific names ( like diameter and radius ) other than a radius and diameter ? |
draw a circle and label the radius , diameter , center and the circumference . let me draw a circle , it wo n't be that well drawn of a circle but i think you get the idea so that is my circle . i 'm going to label the center..over here . so i 'll do the center i 'll call it 'c ' . so that is my center ... .and i 'll d... | draw a circle and label the radius , diameter , center and the circumference . let me draw a circle , it wo n't be that well drawn of a circle but i think you get the idea so that is my circle . i 'm going to label the center..over here . | what is the circumference of the circle ? |
draw a circle and label the radius , diameter , center and the circumference . let me draw a circle , it wo n't be that well drawn of a circle but i think you get the idea so that is my circle . i 'm going to label the center..over here . so i 'll do the center i 'll call it 'c ' . so that is my center ... .and i 'll d... | draw a circle and label the radius , diameter , center and the circumference . let me draw a circle , it wo n't be that well drawn of a circle but i think you get the idea so that is my circle . i 'm going to label the center..over here . | are diameters of the same circle equal if radii of the same circle are equal ? |
draw a circle and label the radius , diameter , center and the circumference . let me draw a circle , it wo n't be that well drawn of a circle but i think you get the idea so that is my circle . i 'm going to label the center..over here . so i 'll do the center i 'll call it 'c ' . so that is my center ... .and i 'll d... | draw a circle and label the radius , diameter , center and the circumference . let me draw a circle , it wo n't be that well drawn of a circle but i think you get the idea so that is my circle . i 'm going to label the center..over here . | how do you find the circumference of the circle and the pi area ? |
draw a circle and label the radius , diameter , center and the circumference . let me draw a circle , it wo n't be that well drawn of a circle but i think you get the idea so that is my circle . i 'm going to label the center..over here . so i 'll do the center i 'll call it 'c ' . so that is my center ... .and i 'll d... | draw a circle and label the radius , diameter , center and the circumference . let me draw a circle , it wo n't be that well drawn of a circle but i think you get the idea so that is my circle . | so the radius is always half of the diameter ? |
draw a circle and label the radius , diameter , center and the circumference . let me draw a circle , it wo n't be that well drawn of a circle but i think you get the idea so that is my circle . i 'm going to label the center..over here . so i 'll do the center i 'll call it 'c ' . so that is my center ... .and i 'll d... | ..which is the same as that distance ! i can draw multiple radii . all of these are radii the distance between the center and any point on the circle now a diameter just goes straight across the circle going throooouugh the center from one side of the circle to the other side..going though the center and it 's essentia... | whats the difference between radius and radii ? |
draw a circle and label the radius , diameter , center and the circumference . let me draw a circle , it wo n't be that well drawn of a circle but i think you get the idea so that is my circle . i 'm going to label the center..over here . so i 'll do the center i 'll call it 'c ' . so that is my center ... .and i 'll d... | so that is my center ... .and i 'll draw an arrow there that is the center..of the circle and actually the circle itself is the set of all points that are a fixed distance away from that center and that fixed distance away , they 're all from that center..that is the radius . so let me draw..the radius . so this distan... | is there a name for half a radius ? |
draw a circle and label the radius , diameter , center and the circumference . let me draw a circle , it wo n't be that well drawn of a circle but i think you get the idea so that is my circle . i 'm going to label the center..over here . so i 'll do the center i 'll call it 'c ' . so that is my center ... .and i 'll d... | all of these are radii the distance between the center and any point on the circle now a diameter just goes straight across the circle going throooouugh the center from one side of the circle to the other side..going though the center and it 's essentially two radii put toghether . so for example this would be a diamet... | also if there are 360 different radii in a circle would n't there be 180 max diameters because the diameter is twice as long as the radius ? |
draw a circle and label the radius , diameter , center and the circumference . let me draw a circle , it wo n't be that well drawn of a circle but i think you get the idea so that is my circle . i 'm going to label the center..over here . so i 'll do the center i 'll call it 'c ' . so that is my center ... .and i 'll d... | draw a circle and label the radius , diameter , center and the circumference . let me draw a circle , it wo n't be that well drawn of a circle but i think you get the idea so that is my circle . i 'm going to label the center..over here . | i need help and now please can someone help me how many radii does a circle have ? |
draw a circle and label the radius , diameter , center and the circumference . let me draw a circle , it wo n't be that well drawn of a circle but i think you get the idea so that is my circle . i 'm going to label the center..over here . so i 'll do the center i 'll call it 'c ' . so that is my center ... .and i 'll d... | draw a circle and label the radius , diameter , center and the circumference . let me draw a circle , it wo n't be that well drawn of a circle but i think you get the idea so that is my circle . i 'm going to label the center..over here . | how many diameters does a circle have ? |
draw a circle and label the radius , diameter , center and the circumference . let me draw a circle , it wo n't be that well drawn of a circle but i think you get the idea so that is my circle . i 'm going to label the center..over here . so i 'll do the center i 'll call it 'c ' . so that is my center ... .and i 'll d... | ..which is the same as that distance ! i can draw multiple radii . all of these are radii the distance between the center and any point on the circle now a diameter just goes straight across the circle going throooouugh the center from one side of the circle to the other side..going though the center and it 's essentia... | so , there can be multiple radius ( or radii or whatever ) and diameters but there 's only one center right ? |
draw a circle and label the radius , diameter , center and the circumference . let me draw a circle , it wo n't be that well drawn of a circle but i think you get the idea so that is my circle . i 'm going to label the center..over here . so i 'll do the center i 'll call it 'c ' . so that is my center ... .and i 'll d... | draw a circle and label the radius , diameter , center and the circumference . let me draw a circle , it wo n't be that well drawn of a circle but i think you get the idea so that is my circle . i 'm going to label the center..over here . | in 3 can a radius come from outside of the circle also ? |
draw a circle and label the radius , diameter , center and the circumference . let me draw a circle , it wo n't be that well drawn of a circle but i think you get the idea so that is my circle . i 'm going to label the center..over here . so i 'll do the center i 'll call it 'c ' . so that is my center ... .and i 'll d... | draw a circle and label the radius , diameter , center and the circumference . let me draw a circle , it wo n't be that well drawn of a circle but i think you get the idea so that is my circle . i 'm going to label the center..over here . | is there a part of a circle called the chord ? |
draw a circle and label the radius , diameter , center and the circumference . let me draw a circle , it wo n't be that well drawn of a circle but i think you get the idea so that is my circle . i 'm going to label the center..over here . so i 'll do the center i 'll call it 'c ' . so that is my center ... .and i 'll d... | all of these are radii the distance between the center and any point on the circle now a diameter just goes straight across the circle going throooouugh the center from one side of the circle to the other side..going though the center and it 's essentially two radii put toghether . so for example this would be a diamet... | how come sometimes when you 're trying out to find the diameter of something , cause i know that diameter = 2 times the radius , say for example , you 're trying to find the diameter of 14pi , you would take half of that and originally multiply it by 2 , but the answer would only result in half the number ( 7 ) ? |
draw a circle and label the radius , diameter , center and the circumference . let me draw a circle , it wo n't be that well drawn of a circle but i think you get the idea so that is my circle . i 'm going to label the center..over here . so i 'll do the center i 'll call it 'c ' . so that is my center ... .and i 'll d... | draw a circle and label the radius , diameter , center and the circumference . let me draw a circle , it wo n't be that well drawn of a circle but i think you get the idea so that is my circle . | i know that pi is approximately 3.141592653589793238462643383279 , but what are tau and e ? |
draw a circle and label the radius , diameter , center and the circumference . let me draw a circle , it wo n't be that well drawn of a circle but i think you get the idea so that is my circle . i 'm going to label the center..over here . so i 'll do the center i 'll call it 'c ' . so that is my center ... .and i 'll d... | draw a circle and label the radius , diameter , center and the circumference . let me draw a circle , it wo n't be that well drawn of a circle but i think you get the idea so that is my circle . | and how and where do we use these irrational numbers ? |
draw a circle and label the radius , diameter , center and the circumference . let me draw a circle , it wo n't be that well drawn of a circle but i think you get the idea so that is my circle . i 'm going to label the center..over here . so i 'll do the center i 'll call it 'c ' . so that is my center ... .and i 'll d... | draw a circle and label the radius , diameter , center and the circumference . let me draw a circle , it wo n't be that well drawn of a circle but i think you get the idea so that is my circle . i 'm going to label the center..over here . | if you want to graph a circle , would that require knowing calculus ? |
draw a circle and label the radius , diameter , center and the circumference . let me draw a circle , it wo n't be that well drawn of a circle but i think you get the idea so that is my circle . i 'm going to label the center..over here . so i 'll do the center i 'll call it 'c ' . so that is my center ... .and i 'll d... | draw a circle and label the radius , diameter , center and the circumference . let me draw a circle , it wo n't be that well drawn of a circle but i think you get the idea so that is my circle . | what is the difference between the perimeter and area ? |
draw a circle and label the radius , diameter , center and the circumference . let me draw a circle , it wo n't be that well drawn of a circle but i think you get the idea so that is my circle . i 'm going to label the center..over here . so i 'll do the center i 'll call it 'c ' . so that is my center ... .and i 'll d... | ..which is the same as that distance ! i can draw multiple radii . all of these are radii the distance between the center and any point on the circle now a diameter just goes straight across the circle going throooouugh the center from one side of the circle to the other side..going though the center and it 's essentia... | are radii the plural of radius ? |
draw a circle and label the radius , diameter , center and the circumference . let me draw a circle , it wo n't be that well drawn of a circle but i think you get the idea so that is my circle . i 'm going to label the center..over here . so i 'll do the center i 'll call it 'c ' . so that is my center ... .and i 'll d... | draw a circle and label the radius , diameter , center and the circumference . let me draw a circle , it wo n't be that well drawn of a circle but i think you get the idea so that is my circle . i 'm going to label the center..over here . so i 'll do the center i 'll call it 'c ' . | however , if you have a circle with its center not marked , and you do n't know and/or can not measure the circumference of the circle , how would you go about locating the center ? |
draw a circle and label the radius , diameter , center and the circumference . let me draw a circle , it wo n't be that well drawn of a circle but i think you get the idea so that is my circle . i 'm going to label the center..over here . so i 'll do the center i 'll call it 'c ' . so that is my center ... .and i 'll d... | draw a circle and label the radius , diameter , center and the circumference . let me draw a circle , it wo n't be that well drawn of a circle but i think you get the idea so that is my circle . | where did tau come from ? |
draw a circle and label the radius , diameter , center and the circumference . let me draw a circle , it wo n't be that well drawn of a circle but i think you get the idea so that is my circle . i 'm going to label the center..over here . so i 'll do the center i 'll call it 'c ' . so that is my center ... .and i 'll d... | draw a circle and label the radius , diameter , center and the circumference . let me draw a circle , it wo n't be that well drawn of a circle but i think you get the idea so that is my circle . i 'm going to label the center..over here . | or in other words is the edge of the circle known as the circumference ? |
draw a circle and label the radius , diameter , center and the circumference . let me draw a circle , it wo n't be that well drawn of a circle but i think you get the idea so that is my circle . i 'm going to label the center..over here . so i 'll do the center i 'll call it 'c ' . so that is my center ... .and i 'll d... | draw a circle and label the radius , diameter , center and the circumference . let me draw a circle , it wo n't be that well drawn of a circle but i think you get the idea so that is my circle . i 'm going to label the center..over here . | does a circle ever have fixed lines of symmetry ? |
draw a circle and label the radius , diameter , center and the circumference . let me draw a circle , it wo n't be that well drawn of a circle but i think you get the idea so that is my circle . i 'm going to label the center..over here . so i 'll do the center i 'll call it 'c ' . so that is my center ... .and i 'll d... | so that is my center ... .and i 'll draw an arrow there that is the center..of the circle and actually the circle itself is the set of all points that are a fixed distance away from that center and that fixed distance away , they 're all from that center..that is the radius . so let me draw..the radius . so this distan... | so the diameter the 2 times the radius or the radius squared ? |
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