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one of the most fundamental ideas in all of physics is the idea of work . now when you first learn work , you just say , oh , that 's just force times distance . but then later on , when you learn a little bit about vectors , you realize that the force is n't always going in the same direction as your displacement . so... | so what would something like this be ? this is a vector field . this is a vector field in 2-dimensional space . | does the function become a vector field when is maps a set of points , 2 or more , to a vector ? |
one of the most fundamental ideas in all of physics is the idea of work . now when you first learn work , you just say , oh , that 's just force times distance . but then later on , when you learn a little bit about vectors , you realize that the force is n't always going in the same direction as your displacement . so... | so let 's say that i have a vector field f , and we 're going to think about what this means in a second . it 's a function of x and y , and it 's equal to some scalar function of x and y times the i-unit vector , or the horizontal unit vector , plus some other function , scalar function of x and y , times the vertical... | does a function become a vector function when it maps a , 1 , scalar to a vector ? |
one of the most fundamental ideas in all of physics is the idea of work . now when you first learn work , you just say , oh , that 's just force times distance . but then later on , when you learn a little bit about vectors , you realize that the force is n't always going in the same direction as your displacement . so... | but the idea of the dot product is , take how much of this vector is going in the same direction as this vector , in this case , this much . and then multiply the two magnitudes . and that 's what we did right here . | how are the two concepts connected ? |
one of the most fundamental ideas in all of physics is the idea of work . now when you first learn work , you just say , oh , that 's just force times distance . but then later on , when you learn a little bit about vectors , you realize that the force is n't always going in the same direction as your displacement . so... | right ? i have a differential , it 's a differential vector , infinitely small displacement . and let 's say over the course of that , the vector field is acting in this local area , let 's say it looks something like that . | and why would the infinitely small change on the curve be called the differential vector/dr ? |
one of the most fundamental ideas in all of physics is the idea of work . now when you first learn work , you just say , oh , that 's just force times distance . but then later on , when you learn a little bit about vectors , you realize that the force is n't always going in the same direction as your displacement . so... | but i think you get the idea . it associates a vector with every point on x-y plane . now , this is called a vector field , so it probably makes a lot of sense that this could be used to describe any type of field . | out of curiosity , are there many applications for dealing with vector fields in the complex plane ? |
one of the most fundamental ideas in all of physics is the idea of work . now when you first learn work , you just say , oh , that 's just force times distance . but then later on , when you learn a little bit about vectors , you realize that the force is n't always going in the same direction as your displacement . so... | but this is essentially all that we have to do . and we 're going to see some concrete examples of taking a line integral through a vector field , or using vector functions , in the next video . | what 's the difference between positon vector valued functions and vector fields ? |
one of the most fundamental ideas in all of physics is the idea of work . now when you first learn work , you just say , oh , that 's just force times distance . but then later on , when you learn a little bit about vectors , you realize that the force is n't always going in the same direction as your displacement . so... | so what would something like this be ? this is a vector field . this is a vector field in 2-dimensional space . | how would i figure out the a position vector function for a particle placed in this vector field ? |
one of the most fundamental ideas in all of physics is the idea of work . now when you first learn work , you just say , oh , that 's just force times distance . but then later on , when you learn a little bit about vectors , you realize that the force is n't always going in the same direction as your displacement . so... | it could be an electric field , it could be a magnetic field . and this could be essentially telling you how much force there would be on some particle in that field . that 's exactly what this would describe . | meaning , if i know the initial position and velocity of a particle placed in this field which is not on tracks how would i calculate where that particle goes and the path it takes ? |
one of the most fundamental ideas in all of physics is the idea of work . now when you first learn work , you just say , oh , that 's just force times distance . but then later on , when you learn a little bit about vectors , you realize that the force is n't always going in the same direction as your displacement . so... | but this is essentially all that we have to do . and we 're going to see some concrete examples of taking a line integral through a vector field , or using vector functions , in the next video . | do the vector fields and vector functions mean the same ? |
one of the most fundamental ideas in all of physics is the idea of work . now when you first learn work , you just say , oh , that 's just force times distance . but then later on , when you learn a little bit about vectors , you realize that the force is n't always going in the same direction as your displacement . so... | it 's a function of x and y , and it 's equal to some scalar function of x and y times the i-unit vector , or the horizontal unit vector , plus some other function , scalar function of x and y , times the vertical unit vector . so what would something like this be ? this is a vector field . | if you were to plot f ( x , y ) on the z axis would you also get a surface like you would if you had a scalar field ? |
one of the most fundamental ideas in all of physics is the idea of work . now when you first learn work , you just say , oh , that 's just force times distance . but then later on , when you learn a little bit about vectors , you realize that the force is n't always going in the same direction as your displacement . so... | but this is essentially all that we have to do . and we 're going to see some concrete examples of taking a line integral through a vector field , or using vector functions , in the next video . | i ca n't find the connection between line integrals for vector fields and line integrals for scalar fields.. are you still finding the area of the so called `` curtain '' when you take the line integral ? |
one of the most fundamental ideas in all of physics is the idea of work . now when you first learn work , you just say , oh , that 's just force times distance . but then later on , when you learn a little bit about vectors , you realize that the force is n't always going in the same direction as your displacement . so... | and if you just think about it , what is f dot r ? or what is f dot dr ? well , actually , to answer that , let 's remember what dr looked like . | when taking the dot product of f.dr , where is the cos ( theta ) necessary to properly attribute the correct proportion of force moving the the direction of dr ? |
one of the most fundamental ideas in all of physics is the idea of work . now when you first learn work , you just say , oh , that 's just force times distance . but then later on , when you learn a little bit about vectors , you realize that the force is n't always going in the same direction as your displacement . so... | but i think you get the idea . it associates a vector with every point on x-y plane . now , this is called a vector field , so it probably makes a lot of sense that this could be used to describe any type of field . | the position vector r is a vector that goes from the origin to te point x ( t ) , y ( t ) ? |
one of the most fundamental ideas in all of physics is the idea of work . now when you first learn work , you just say , oh , that 's just force times distance . but then later on , when you learn a little bit about vectors , you realize that the force is n't always going in the same direction as your displacement . so... | we want to sum up all of the drs to figure out the total , all of the f dot drs to figure out the total work done . and that 's where the integral comes in . we will do a line integral over -- i mean , you could think of it two ways . | in the end , why is the integral in du equal to the integral in dt , considering that they are different variables ? |
one of the most fundamental ideas in all of physics is the idea of work . now when you first learn work , you just say , oh , that 's just force times distance . but then later on , when you learn a little bit about vectors , you realize that the force is n't always going in the same direction as your displacement . so... | well , it 's essentially saying , look . you give me any x , any y , you give any x , y in the x-y plane , and these are going to end up with some numbers , right ? when you put x , y here , you 're going to get some value , when you put x , y here , you 're going to get some value . | and give the strength of the lines resistance to change a constant value given rise to the end result ? |
one of the most fundamental ideas in all of physics is the idea of work . now when you first learn work , you just say , oh , that 's just force times distance . but then later on , when you learn a little bit about vectors , you realize that the force is n't always going in the same direction as your displacement . so... | we want to sum up all of the drs to figure out the total , all of the f dot drs to figure out the total work done . and that 's where the integral comes in . we will do a line integral over -- i mean , you could think of it two ways . you could write just d dot w there , but we could say , we 'll do a line integral alo... | is n't a line integral the area of a `` wall '' between a path and a surface above it ? |
one of the most fundamental ideas in all of physics is the idea of work . now when you first learn work , you just say , oh , that 's just force times distance . but then later on , when you learn a little bit about vectors , you realize that the force is n't always going in the same direction as your displacement . so... | maybe when i go here , the victor looks like this . maybe when i go here , the vector looks like that . and maybe when i go up here , the vector goes like that . | at the ending formula where does the vector notation ( i , j ) go ? |
one of the most fundamental ideas in all of physics is the idea of work . now when you first learn work , you just say , oh , that 's just force times distance . but then later on , when you learn a little bit about vectors , you realize that the force is n't always going in the same direction as your displacement . so... | and we know what that is , just from this example up here . that 's the dot product . it 's the dot product of the force and our super-small displacement . | when sal is doing that dot product at the end , why is n't cos ( theta ) being multiplied by everything ? |
one of the most fundamental ideas in all of physics is the idea of work . now when you first learn work , you just say , oh , that 's just force times distance . but then later on , when you learn a little bit about vectors , you realize that the force is n't always going in the same direction as your displacement . so... | you could say , what 's the small interval of work ? you could say d work , or a differential of work . well , by the same exact logic that we did with the simple problem , it 's the magnitude of the force in the direction of our displacement times the magnitude of our displacement . | i do n't take physics , can someone explain what `` work '' is ? |
one of the most fundamental ideas in all of physics is the idea of work . now when you first learn work , you just say , oh , that 's just force times distance . but then later on , when you learn a little bit about vectors , you realize that the force is n't always going in the same direction as your displacement . so... | so what would something like this be ? this is a vector field . this is a vector field in 2-dimensional space . | so a line integral of a vector field can be thought as the sum of all of the vectors of the vector field acting on the curve ? |
one of the most fundamental ideas in all of physics is the idea of work . now when you first learn work , you just say , oh , that 's just force times distance . but then later on , when you learn a little bit about vectors , you realize that the force is n't always going in the same direction as your displacement . so... | but this is essentially all that we have to do . and we 're going to see some concrete examples of taking a line integral through a vector field , or using vector functions , in the next video . | so , a line integral over a vector field is a summation of dot product of two vectors ( along a curve ) ? |
one of the most fundamental ideas in all of physics is the idea of work . now when you first learn work , you just say , oh , that 's just force times distance . but then later on , when you learn a little bit about vectors , you realize that the force is n't always going in the same direction as your displacement . so... | and if you just think about it , what is f dot r ? or what is f dot dr ? well , actually , to answer that , let 's remember what dr looked like . | what is the connection between ds and dr ? |
one of the most fundamental ideas in all of physics is the idea of work . now when you first learn work , you just say , oh , that 's just force times distance . but then later on , when you learn a little bit about vectors , you realize that the force is n't always going in the same direction as your displacement . so... | at any point , if you happen to have something there . maybe that 's what the function is . and i could keep doing this forever , and filling in all the gaps . | can we evaluate line integrals without parametrizing paths as a function of time ? |
one of the most fundamental ideas in all of physics is the idea of work . now when you first learn work , you just say , oh , that 's just force times distance . but then later on , when you learn a little bit about vectors , you realize that the force is n't always going in the same direction as your displacement . so... | my object is changing direction . so let 's say when i 'm here , and let 's say i move a small amount of my path . so let 's say i move , this is an infinitesimally small dr . | let 's say i just wanted to take the line integral over the path defined by y = x^2 ? |
one of the most fundamental ideas in all of physics is the idea of work . now when you first learn work , you just say , oh , that 's just force times distance . but then later on , when you learn a little bit about vectors , you realize that the force is n't always going in the same direction as your displacement . so... | we want to sum up all of the drs to figure out the total , all of the f dot drs to figure out the total work done . and that 's where the integral comes in . we will do a line integral over -- i mean , you could think of it two ways . you could write just d dot w there , but we could say , we 'll do a line integral alo... | why do we use the pythagorean theorem to determine ds in the initial line integral videos for the length of the parametrized curve while here we just use the derivative for displacement ? |
one of the most fundamental ideas in all of physics is the idea of work . now when you first learn work , you just say , oh , that 's just force times distance . but then later on , when you learn a little bit about vectors , you realize that the force is n't always going in the same direction as your displacement . so... | so what would something like this be ? this is a vector field . this is a vector field in 2-dimensional space . | 1. so what 's the difference between an equation modelling a vector field f ( x , y ) and a vector position function ( r ) they both give you vector why is there distinction between the two are there any differences ? |
one of the most fundamental ideas in all of physics is the idea of work . now when you first learn work , you just say , oh , that 's just force times distance . but then later on , when you learn a little bit about vectors , you realize that the force is n't always going in the same direction as your displacement . so... | so let 's say i move , this is an infinitesimally small dr . right ? i have a differential , it 's a differential vector , infinitely small displacement . | vector fields can also be done in 3 dimensions right ? |
one of the most fundamental ideas in all of physics is the idea of work . now when you first learn work , you just say , oh , that 's just force times distance . but then later on , when you learn a little bit about vectors , you realize that the force is n't always going in the same direction as your displacement . so... | when you put x , y here , you 're going to get some value , when you put x , y here , you 're going to get some value . so you 're going to get some combination of the i- and j-unit vectors . so you 're going to get some vector . | why do n't we include the unit vectors in the integral ? |
one of the most fundamental ideas in all of physics is the idea of work . now when you first learn work , you just say , oh , that 's just force times distance . but then later on , when you learn a little bit about vectors , you realize that the force is n't always going in the same direction as your displacement . so... | the work is equal to the 5 newtons . that was the magnitude of my force vector , so it 's the magnitude of my force vector , times the cosine of this angle . so you know , let 's call that theta . | is the magnitude of the vector 's y component defined as torque ? |
one of the most fundamental ideas in all of physics is the idea of work . now when you first learn work , you just say , oh , that 's just force times distance . but then later on , when you learn a little bit about vectors , you realize that the force is n't always going in the same direction as your displacement . so... | hopefully you realize i could have just kept writing , but i 'm running out of space . plus q of x of t , y of t , times the component of our dr. times the y-component , or the j-component . y prime of t dt . | what is the length of the northern component of a + b ? |
one of the most fundamental ideas in all of physics is the idea of work . now when you first learn work , you just say , oh , that 's just force times distance . but then later on , when you learn a little bit about vectors , you realize that the force is n't always going in the same direction as your displacement . so... | so what would something like this be ? this is a vector field . this is a vector field in 2-dimensional space . | ( quoting paulo constantino 's question , but adding more to it ) could you calculate the path that it would take if it was pushed around by the vector field ? |
one of the most fundamental ideas in all of physics is the idea of work . now when you first learn work , you just say , oh , that 's just force times distance . but then later on , when you learn a little bit about vectors , you realize that the force is n't always going in the same direction as your displacement . so... | so what would something like this be ? this is a vector field . this is a vector field in 2-dimensional space . | is this vector field in three dimensions since it is a function of two variables ? |
in the last video , we learned , or at least i showed you . i do n't know if you 've learned it yet but we 'll learn it in this video but we learned that the force on a moving charge , from a magnetic field , when it 's a vector quantity , is equal to the charge on the moving charge times the cross product of the velo... | my hand is brown , so my right hand is going to look something like this . my index finger is pointing in the direction of the velocity vector while my middle finger is pointing in the direction of the magnetic field , so my index finger is going to point straight up , so all you see is the tip of it , and then my othe... | how on earth are his middle finger and thumb able to bend in opposite directions ? |
in the last video , we learned , or at least i showed you . i do n't know if you 've learned it yet but we 'll learn it in this video but we learned that the force on a moving charge , from a magnetic field , when it 's a vector quantity , is equal to the charge on the moving charge times the cross product of the velo... | i 'll write that down right now . sine of the angle between them . but let me ask you a question . | i thought cross products were done with cosine and dot products with sine , am i incorrect ? |
in the last video , we learned , or at least i showed you . i do n't know if you 've learned it yet but we 'll learn it in this video but we learned that the force on a moving charge , from a magnetic field , when it 's a vector quantity , is equal to the charge on the moving charge times the cross product of the velo... | it 's popping out , and so if i arrange my right hand like that , my thumb points down , so this is the direction of the force . so as this particle moves to the right with some velocity , there 's actually going to be a downward force , downward on this plane , so the force is going to move in this direction and so wh... | so i understand tht the particle moves in a circle , but is it in the same plane or does it spiral in the direction of the feild lines ? |
in the last video , we learned , or at least i showed you . i do n't know if you 've learned it yet but we 'll learn it in this video but we learned that the force on a moving charge , from a magnetic field , when it 's a vector quantity , is equal to the charge on the moving charge times the cross product of the velo... | well think about it . if you have a force here and the velocity 's like that , if the particles , it 'll be deflected a little bit to the right , and then , since the force is always going to be perpendicular to the velocity vector , the force is going to charge like that , so the particle is actually going to go in a ... | basically , is the shape of the particles path a flat disk or a spring ? |
what i want to do in this video is get some practice , or become familiar with what different angle measures in radians actually represent . and to get our familiarity , we 're gon na start with a ray that starts at the origin , and moves along , and ... not moves , and points along the positive x axis . we 're gon na... | two pi over seven , do we even get past pi over two ? pi over two here would be 3.5 pi over seven . we do n't even get to pi over two . | he writes the value of pi = 3.14 , but sal uses it as a reference for radians , is n't the 3.14 value in degrees ? |
what i want to do in this video is get some practice , or become familiar with what different angle measures in radians actually represent . and to get our familiarity , we 're gon na start with a ray that starts at the origin , and moves along , and ... not moves , and points along the positive x axis . we 're gon na... | if we were to go , essentially , be pointed in the opposite direction . instead of being pointed to the right , making a full , i guess you could say 180 degree counterclockwise rotation , that would be pi radians . that would be pi radians . | why is a 90 degree rotation pi over 2 ? |
what i want to do in this video is get some practice , or become familiar with what different angle measures in radians actually represent . and to get our familiarity , we 're gon na start with a ray that starts at the origin , and moves along , and ... not moves , and points along the positive x axis . we 're gon na... | instead of being pointed to the right , making a full , i guess you could say 180 degree counterclockwise rotation , that would be pi radians . that would be pi radians . but this thing is less than pi . | why is 90 degrees equal to pi/2 radians ? |
what i want to do in this video is get some practice , or become familiar with what different angle measures in radians actually represent . and to get our familiarity , we 're gon na start with a ray that starts at the origin , and moves along , and ... not moves , and points along the positive x axis . we 're gon na... | what i want to do in this video is get some practice , or become familiar with what different angle measures in radians actually represent . and to get our familiarity , we 're gon na start with a ray that starts at the origin , and moves along , and ... not moves , and points along the positive x axis . | are these units also useful for mathematics ? |
what i want to do in this video is get some practice , or become familiar with what different angle measures in radians actually represent . and to get our familiarity , we 're gon na start with a ray that starts at the origin , and moves along , and ... not moves , and points along the positive x axis . we 're gon na... | instead of being pointed to the right , making a full , i guess you could say 180 degree counterclockwise rotation , that would be pi radians . that would be pi radians . but this thing is less than pi . | what quadrant is pi radians in ? |
what i want to do in this video is get some practice , or become familiar with what different angle measures in radians actually represent . and to get our familiarity , we 're gon na start with a ray that starts at the origin , and moves along , and ... not moves , and points along the positive x axis . we 're gon na... | that would be pi radians . but this thing is less than pi . pi would be five pi over five . this is less than pi radians . we are going to sit , we are going to sit someplace , someplace , and i 'm just estimating it . | how do you know that 2pi/7 is less than pi/2 ? |
what i want to do in this video is get some practice , or become familiar with what different angle measures in radians actually represent . and to get our familiarity , we 're gon na start with a ray that starts at the origin , and moves along , and ... not moves , and points along the positive x axis . we 're gon na... | this is gon na throw us in the first quadrant . what about three radians ? one way to think about it is , three is a little bit less than pi . | what would three radian be in terms of degrees ? |
what i want to do in this video is get some practice , or become familiar with what different angle measures in radians actually represent . and to get our familiarity , we 're gon na start with a ray that starts at the origin , and moves along , and ... not moves , and points along the positive x axis . we 're gon na... | instead of being pointed to the right , making a full , i guess you could say 180 degree counterclockwise rotation , that would be pi radians . that would be pi radians . but this thing is less than pi . | so if you have -5pi/6 that would be in the third quadrant close to the x-axis ? |
what i want to do in this video is get some practice , or become familiar with what different angle measures in radians actually represent . and to get our familiarity , we 're gon na start with a ray that starts at the origin , and moves along , and ... not moves , and points along the positive x axis . we 're gon na... | if we were to go , essentially , be pointed in the opposite direction . instead of being pointed to the right , making a full , i guess you could say 180 degree counterclockwise rotation , that would be pi radians . that would be pi radians . but this thing is less than pi . pi would be five pi over five . this is less... | and also how 180 degrees is pi ? |
what i want to do in this video is get some practice , or become familiar with what different angle measures in radians actually represent . and to get our familiarity , we 're gon na start with a ray that starts at the origin , and moves along , and ... not moves , and points along the positive x axis . we 're gon na... | and so we are going to sit in the second quadrant . let 's think about two pi seven . two pi over seven , do we even get past pi over two ? pi over two here would be 3.5 pi over seven . | so would there be a good way to remember how , say , two pi over seven radians is less then pi over two ? |
what i want to do in this video is get some practice , or become familiar with what different angle measures in radians actually represent . and to get our familiarity , we 're gon na start with a ray that starts at the origin , and moves along , and ... not moves , and points along the positive x axis . we 're gon na... | instead of being pointed to the right , making a full , i guess you could say 180 degree counterclockwise rotation , that would be pi radians . that would be pi radians . but this thing is less than pi . | how would we find the quadrant , and/or a point that intersects with the arc length on a unit cirlce ? |
what i want to do in this video is get some practice , or become familiar with what different angle measures in radians actually represent . and to get our familiarity , we 're gon na start with a ray that starts at the origin , and moves along , and ... not moves , and points along the positive x axis . we 're gon na... | what i want to do in this video is get some practice , or become familiar with what different angle measures in radians actually represent . and to get our familiarity , we 're gon na start with a ray that starts at the origin , and moves along , and ... not moves , and points along the positive x axis . | 0 can someone explain to me how big 1 radian is ? |
what i want to do in this video is get some practice , or become familiar with what different angle measures in radians actually represent . and to get our familiarity , we 're gon na start with a ray that starts at the origin , and moves along , and ... not moves , and points along the positive x axis . we 're gon na... | instead of being pointed to the right , making a full , i guess you could say 180 degree counterclockwise rotation , that would be pi radians . that would be pi radians . but this thing is less than pi . pi would be five pi over five . this is less than pi radians . | what is pi/2 supposed to mean ? |
what i want to do in this video is get some practice , or become familiar with what different angle measures in radians actually represent . and to get our familiarity , we 're gon na start with a ray that starts at the origin , and moves along , and ... not moves , and points along the positive x axis . we 're gon na... | instead of being pointed to the right , making a full , i guess you could say 180 degree counterclockwise rotation , that would be pi radians . that would be pi radians . but this thing is less than pi . pi would be five pi over five . this is less than pi radians . | if the positive x axis is pi/2 then what is the negative y and negative x ? |
what i want to do in this video is get some practice , or become familiar with what different angle measures in radians actually represent . and to get our familiarity , we 're gon na start with a ray that starts at the origin , and moves along , and ... not moves , and points along the positive x axis . we 're gon na... | instead of being pointed to the right , making a full , i guess you could say 180 degree counterclockwise rotation , that would be pi radians . that would be pi radians . but this thing is less than pi . pi would be five pi over five . this is less than pi radians . | how is ( 2pi/7 ) smaller than ( pi/2 ) ? |
what i want to do in this video is get some practice , or become familiar with what different angle measures in radians actually represent . and to get our familiarity , we 're gon na start with a ray that starts at the origin , and moves along , and ... not moves , and points along the positive x axis . we 're gon na... | instead of being pointed to the right , making a full , i guess you could say 180 degree counterclockwise rotation , that would be pi radians . that would be pi radians . but this thing is less than pi . pi would be five pi over five . this is less than pi radians . | how do i input pi symbol in answer parts ? |
what i want to do in this video is get some practice , or become familiar with what different angle measures in radians actually represent . and to get our familiarity , we 're gon na start with a ray that starts at the origin , and moves along , and ... not moves , and points along the positive x axis . we 're gon na... | and to get our familiarity , we 're gon na start with a ray that starts at the origin , and moves along , and ... not moves , and points along the positive x axis . we 're gon na start with this magenta ray , and we 're gon na rotate it around the origin counterclockwise by different angle measures . and think about wh... | since rotating clockwise or counter-clockwise around the origin would provide different results ; what 's the reason sal rotates counter-clockwise ? |
what i want to do in this video is get some practice , or become familiar with what different angle measures in radians actually represent . and to get our familiarity , we 're gon na start with a ray that starts at the origin , and moves along , and ... not moves , and points along the positive x axis . we 're gon na... | what i want to do in this video is get some practice , or become familiar with what different angle measures in radians actually represent . and to get our familiarity , we 're gon na start with a ray that starts at the origin , and moves along , and ... not moves , and points along the positive x axis . we 're gon na... | why anti-clockwise angle is positive ? |
what i want to do in this video is get some practice , or become familiar with what different angle measures in radians actually represent . and to get our familiarity , we 're gon na start with a ray that starts at the origin , and moves along , and ... not moves , and points along the positive x axis . we 're gon na... | this thing is less than pi over two . this is gon na throw us in the first quadrant . what about three radians ? | to which quadrant will 720 degree take us ? |
what i want to do in this video is get some practice , or become familiar with what different angle measures in radians actually represent . and to get our familiarity , we 're gon na start with a ray that starts at the origin , and moves along , and ... not moves , and points along the positive x axis . we 're gon na... | this is gon na throw us in the first quadrant . what about three radians ? one way to think about it is , three is a little bit less than pi . | what is the relationship of radians to degrees ? |
what i want to do in this video is get some practice , or become familiar with what different angle measures in radians actually represent . and to get our familiarity , we 're gon na start with a ray that starts at the origin , and moves along , and ... not moves , and points along the positive x axis . we 're gon na... | three pi over five , so we 're gon na start rotating . if we go straight up , if we rotate it , essentially , if you want to think in degrees , if you rotate it counterclockwise 90 degrees , that is going to get us to pi over two . that would have been a counterclockwise rotation of pi over two radians . | how many degrees in one radian ? |
what i want to do in this video is get some practice , or become familiar with what different angle measures in radians actually represent . and to get our familiarity , we 're gon na start with a ray that starts at the origin , and moves along , and ... not moves , and points along the positive x axis . we 're gon na... | instead of being pointed to the right , making a full , i guess you could say 180 degree counterclockwise rotation , that would be pi radians . that would be pi radians . but this thing is less than pi . | so if we have to solve a question like 5 radians , where there is no pi , do we just compare it do normal values such as pi and 2pi ? |
what i want to do in this video is get some practice , or become familiar with what different angle measures in radians actually represent . and to get our familiarity , we 're gon na start with a ray that starts at the origin , and moves along , and ... not moves , and points along the positive x axis . we 're gon na... | what i want to do in this video is get some practice , or become familiar with what different angle measures in radians actually represent . and to get our familiarity , we 're gon na start with a ray that starts at the origin , and moves along , and ... not moves , and points along the positive x axis . | how do i demonstrate 1/7 of the circuference of a circle ? |
what i want to do in this video is get some practice , or become familiar with what different angle measures in radians actually represent . and to get our familiarity , we 're gon na start with a ray that starts at the origin , and moves along , and ... not moves , and points along the positive x axis . we 're gon na... | this is gon na throw us in the first quadrant . what about three radians ? one way to think about it is , three is a little bit less than pi . | how exactly do you convert 3 radians to degrees ? |
what i want to do in this video is get some practice , or become familiar with what different angle measures in radians actually represent . and to get our familiarity , we 're gon na start with a ray that starts at the origin , and moves along , and ... not moves , and points along the positive x axis . we 're gon na... | instead of being pointed to the right , making a full , i guess you could say 180 degree counterclockwise rotation , that would be pi radians . that would be pi radians . but this thing is less than pi . | what would be the conditions for a ray with a certain value of radian to lie in the 3rd or 4th quadrant ? |
what i want to do in this video is get some practice , or become familiar with what different angle measures in radians actually represent . and to get our familiarity , we 're gon na start with a ray that starts at the origin , and moves along , and ... not moves , and points along the positive x axis . we 're gon na... | three is less than pi but it 's greater than pi over two . how do we know that ? well , pi is approximately 3.14159 and it just keeps going on and on forever . | how did you know 3pi etc is there and so on ? |
what i want to do in this video is get some practice , or become familiar with what different angle measures in radians actually represent . and to get our familiarity , we 're gon na start with a ray that starts at the origin , and moves along , and ... not moves , and points along the positive x axis . we 're gon na... | what i want to do in this video is get some practice , or become familiar with what different angle measures in radians actually represent . and to get our familiarity , we 're gon na start with a ray that starts at the origin , and moves along , and ... not moves , and points along the positive x axis . | a train is moving on a circular curve of radius 1500m at the rate of 66km/hour.through what angle has it turned in 10 seconds ? |
what i want to do in this video is get some practice , or become familiar with what different angle measures in radians actually represent . and to get our familiarity , we 're gon na start with a ray that starts at the origin , and moves along , and ... not moves , and points along the positive x axis . we 're gon na... | what i want to do in this video is get some practice , or become familiar with what different angle measures in radians actually represent . and to get our familiarity , we 're gon na start with a ray that starts at the origin , and moves along , and ... not moves , and points along the positive x axis . | how is khan able to understand that the particular radin measure is in which coordinate ? |
what i want to do in this video is get some practice , or become familiar with what different angle measures in radians actually represent . and to get our familiarity , we 're gon na start with a ray that starts at the origin , and moves along , and ... not moves , and points along the positive x axis . we 're gon na... | two pi over seven , do we even get past pi over two ? pi over two here would be 3.5 pi over seven . we do n't even get to pi over two . | why 3 pi was not exactly at the same place as the x-axis according to pi=180 degrees ? |
what i want to do in this video is get some practice , or become familiar with what different angle measures in radians actually represent . and to get our familiarity , we 're gon na start with a ray that starts at the origin , and moves along , and ... not moves , and points along the positive x axis . we 're gon na... | assume you 've paused the video , and you 've tried it out on your own , so let 's try this first one , three pi over five . three pi over five , so we 're gon na start rotating . if we go straight up , if we rotate it , essentially , if you want to think in degrees , if you rotate it counterclockwise 90 degrees , that... | how is sal rotating the line ? |
what i want to do in this video is get some practice , or become familiar with what different angle measures in radians actually represent . and to get our familiarity , we 're gon na start with a ray that starts at the origin , and moves along , and ... not moves , and points along the positive x axis . we 're gon na... | instead of being pointed to the right , making a full , i guess you could say 180 degree counterclockwise rotation , that would be pi radians . that would be pi radians . but this thing is less than pi . pi would be five pi over five . this is less than pi radians . | how does sal know that it is pi/2 ? |
what i want to do in this video is get some practice , or become familiar with what different angle measures in radians actually represent . and to get our familiarity , we 're gon na start with a ray that starts at the origin , and moves along , and ... not moves , and points along the positive x axis . we 're gon na... | and so we are going to sit in the second quadrant . let 's think about two pi seven . two pi over seven , do we even get past pi over two ? pi over two here would be 3.5 pi over seven . we do n't even get to pi over two . | at 0 sal says that pi/2 there is equal to 3.5 pi over seven , how does that work out ? |
what i want to do in this video is get some practice , or become familiar with what different angle measures in radians actually represent . and to get our familiarity , we 're gon na start with a ray that starts at the origin , and moves along , and ... not moves , and points along the positive x axis . we 're gon na... | this thing is less than pi over two . this is gon na throw us in the first quadrant . what about three radians ? | is it necessary to check the quadrant through graph can not we just break the angle into multiple of 360 ? |
what i want to do in this video is get some practice , or become familiar with what different angle measures in radians actually represent . and to get our familiarity , we 're gon na start with a ray that starts at the origin , and moves along , and ... not moves , and points along the positive x axis . we 're gon na... | three is less than pi but it 's greater than pi over two . how do we know that ? well , pi is approximately 3.14159 and it just keeps going on and on forever . | how do we know 3 is less than pie ? |
what i want to do in this video is get some practice , or become familiar with what different angle measures in radians actually represent . and to get our familiarity , we 're gon na start with a ray that starts at the origin , and moves along , and ... not moves , and points along the positive x axis . we 're gon na... | this is gon na throw us in the first quadrant . what about three radians ? one way to think about it is , three is a little bit less than pi . | radians measure were derived from circles then how are we plotting them on a plane without any circle ? |
what i want to do in this video is get some practice , or become familiar with what different angle measures in radians actually represent . and to get our familiarity , we 're gon na start with a ray that starts at the origin , and moves along , and ... not moves , and points along the positive x axis . we 're gon na... | if we were to go , essentially , be pointed in the opposite direction . instead of being pointed to the right , making a full , i guess you could say 180 degree counterclockwise rotation , that would be pi radians . that would be pi radians . but this thing is less than pi . | could someone tell me how 3 radians fall in 2nd quadrant if pi is considered 180 ? |
what i want to do in this video is get some practice , or become familiar with what different angle measures in radians actually represent . and to get our familiarity , we 're gon na start with a ray that starts at the origin , and moves along , and ... not moves , and points along the positive x axis . we 're gon na... | what i want to do in this video is get some practice , or become familiar with what different angle measures in radians actually represent . and to get our familiarity , we 're gon na start with a ray that starts at the origin , and moves along , and ... not moves , and points along the positive x axis . we 're gon na... | is quad 1 called 1 because all the values are positive ? |
what i want to do in this video is get some practice , or become familiar with what different angle measures in radians actually represent . and to get our familiarity , we 're gon na start with a ray that starts at the origin , and moves along , and ... not moves , and points along the positive x axis . we 're gon na... | instead of being pointed to the right , making a full , i guess you could say 180 degree counterclockwise rotation , that would be pi radians . that would be pi radians . but this thing is less than pi . | wait , would n't 3pi radians end up in the middle of quadrants 2 & 3 ? |
what i want to do in this video is get some practice , or become familiar with what different angle measures in radians actually represent . and to get our familiarity , we 're gon na start with a ray that starts at the origin , and moves along , and ... not moves , and points along the positive x axis . we 're gon na... | this is gon na throw us in the first quadrant . what about three radians ? one way to think about it is , three is a little bit less than pi . | what is the degree for radians of -2/3pie ? |
what i want to do in this video is get some practice , or become familiar with what different angle measures in radians actually represent . and to get our familiarity , we 're gon na start with a ray that starts at the origin , and moves along , and ... not moves , and points along the positive x axis . we 're gon na... | this is gon na throw us in the first quadrant . what about three radians ? one way to think about it is , three is a little bit less than pi . | how complected is it to just turn degrees from radians ? |
what i want to do in this video is get some practice , or become familiar with what different angle measures in radians actually represent . and to get our familiarity , we 're gon na start with a ray that starts at the origin , and moves along , and ... not moves , and points along the positive x axis . we 're gon na... | and to get our familiarity , we 're gon na start with a ray that starts at the origin , and moves along , and ... not moves , and points along the positive x axis . we 're gon na start with this magenta ray , and we 're gon na rotate it around the origin counterclockwise by different angle measures . and think about wh... | what is a magenta ray ? |
so we 're gon na talk a little bit about dna regulation . and this is the general idea that if you look at a organism 's genome , that not all of the genes are being transcribed and translated at the same time . it could actually depend on the type of cell that that dna is inside of , or it could depend on the environ... | and when you have a promoter associated with multiple genes , that combination of the promoter and the genes , and once again when i 'm talking about the promoters of the genes i 'm talking about sequences of dna , that combination is called an operon . this is called an opeon . it 's a combination of that regulatory d... | what is the location the activator binds in called ? |
so we 're gon na talk a little bit about dna regulation . and this is the general idea that if you look at a organism 's genome , that not all of the genes are being transcribed and translated at the same time . it could actually depend on the type of cell that that dna is inside of , or it could depend on the environ... | so dna is the same inside , and these are going to be , these are eukaryotes , so i 'll draw the nuclear membrane there , same dna . but they have very different roles inside of this organism . so it does n't make sense , in fact , in order for them to even have different structures , they 're gon na have to produce di... | how can completely different types of cell share the same genome ? |
so we 're gon na talk a little bit about dna regulation . and this is the general idea that if you look at a organism 's genome , that not all of the genes are being transcribed and translated at the same time . it could actually depend on the type of cell that that dna is inside of , or it could depend on the environ... | that you have a gene that is a sequence of dna that 's part of the broader chromosome , and we said , `` okay , that rna polymerase needs to attach some place , '' so that rna polymerase needs to attach some place , and we called that place that the rna polymerase attaches , we call that the promoter , and then the pol... | why do cells need to control gene expression ? |
so we 're gon na talk a little bit about dna regulation . and this is the general idea that if you look at a organism 's genome , that not all of the genes are being transcribed and translated at the same time . it could actually depend on the type of cell that that dna is inside of , or it could depend on the environ... | that you have a gene that is a sequence of dna that 's part of the broader chromosome , and we said , `` okay , that rna polymerase needs to attach some place , '' so that rna polymerase needs to attach some place , and we called that place that the rna polymerase attaches , we call that the promoter , and then the pol... | when a gene is said to be expressed ? |
so we 're gon na talk a little bit about dna regulation . and this is the general idea that if you look at a organism 's genome , that not all of the genes are being transcribed and translated at the same time . it could actually depend on the type of cell that that dna is inside of , or it could depend on the environ... | well then we might , something in our environment might allow repressors to take action . so what are we talking about a repressor ? well a repressor , a repressor right over here , you see it attaching to a sequence of dna after the promoter , and so it blocks , it blocks the rna polymerase from being able to do the t... | how do you get rid of the repressor ? |
so we 're gon na talk a little bit about dna regulation . and this is the general idea that if you look at a organism 's genome , that not all of the genes are being transcribed and translated at the same time . it could actually depend on the type of cell that that dna is inside of , or it could depend on the environ... | so the promoter , so that 's this part right over here , that 's the sequence . that is a regulatory , regulatory dna sequence . well that 's what the rna polymerase , which i drew as this big blob , it 's protein here , this big blob , will attach to , and then it will begin to transcribe all of these genes as a bundl... | can the promotor site also be the dna sequence for the repressor protein ? |
so we 're gon na talk a little bit about dna regulation . and this is the general idea that if you look at a organism 's genome , that not all of the genes are being transcribed and translated at the same time . it could actually depend on the type of cell that that dna is inside of , or it could depend on the environ... | that you have a gene that is a sequence of dna that 's part of the broader chromosome , and we said , `` okay , that rna polymerase needs to attach some place , '' so that rna polymerase needs to attach some place , and we called that place that the rna polymerase attaches , we call that the promoter , and then the pol... | how i confirm that a gene has been cloned sucessfully ? |
we 're told that f of seven is equal to 40 plus five , e to the seventh power , and f prime of x is equal to five , e to the x . what is f of zero ? so to evaluate f of zero , let 's take the anti-derivative of f prime of x , and then we 're going to have a constant of integration there , so we can use the information... | so if f prime of x is equal to five , e to the x , then f of x is going to be equal to the anti-derivative of f prime of x , or the anti-derivative of five , e to the x , dx , and this is the thing that i always find amazing about exponentials , and actually , let me just take a step . i 'll take that five out of the i... | 2 , how is it allowed to 'take a constant out of the integral sign ' ? |
we 're told that f of seven is equal to 40 plus five , e to the seventh power , and f prime of x is equal to five , e to the x . what is f of zero ? so to evaluate f of zero , let 's take the anti-derivative of f prime of x , and then we 're going to have a constant of integration there , so we can use the information... | well , it is an expression , but it 's really just a number . there 's no variables in this , and so we can use that to solve for our constant of integration , and then we will have fully known what f of x is , and we can use that to evaluate f of zero , so let 's just do it . so if f prime of x is equal to five , e to... | what if you want to integrate an equation that has the variable in its exponent , and is also being multiplied with a constant ? |
we 're told that f of seven is equal to 40 plus five , e to the seventh power , and f prime of x is equal to five , e to the x . what is f of zero ? so to evaluate f of zero , let 's take the anti-derivative of f prime of x , and then we 're going to have a constant of integration there , so we can use the information... | we 're told that f of seven is equal to 40 plus five , e to the seventh power , and f prime of x is equal to five , e to the x . what is f of zero ? | so what should i target in order to comprehend the famous problem quicker ? |
in the last video we saw that if we had a market with perfect competition , and if the current short-term equilibrium price is above the price the necessary or is above the price at which firms would be generating economic profit , then more and more firms would start entering . because if the economic profit is positi... | even though they 're already making some economic profit , they might determine , hey , we can make even more economic profit if we lower the quantity offered even more . so they might even take supply out of the market . and so they could have a new supply curve that looks like this . | are there any current examples of monopolies resulting in a free market ? |
in the last video we saw that if we had a market with perfect competition , and if the current short-term equilibrium price is above the price the necessary or is above the price at which firms would be generating economic profit , then more and more firms would start entering . because if the economic profit is positi... | you 're not going to have this trend where more and more supply gets on the market until you get to this long-run supply curve . in fact , there will not be this long-run supply curve . the long-run supply curve is whatever , frankly , the monopolist decides they want to do . | how long is the short run and the long run ? |
in the last video we saw that if we had a market with perfect competition , and if the current short-term equilibrium price is above the price the necessary or is above the price at which firms would be generating economic profit , then more and more firms would start entering . because if the economic profit is positi... | because depending on whether the equilibrium price is above or below this , at some point , supply will enter or exit the system so that we eventually get back to some point along this long-run supply curve right over here . now , this was assuming perfect competition . many players , identical products , we did it for... | how is a monopolist system different from communist system , in terms of competition in market ? |
in the last video we saw that if we had a market with perfect competition , and if the current short-term equilibrium price is above the price the necessary or is above the price at which firms would be generating economic profit , then more and more firms would start entering . because if the economic profit is positi... | now when we do that , when we talk about one player as the only player in the market , we are not talking about perfect competition . we are then talking about a monopoly . and it is the same word as perhaps one of your favorite board games . | in what conditions can monopoly occur ? |
in the last video we saw that if we had a market with perfect competition , and if the current short-term equilibrium price is above the price the necessary or is above the price at which firms would be generating economic profit , then more and more firms would start entering . because if the economic profit is positi... | now when we do that , when we talk about one player as the only player in the market , we are not talking about perfect competition . we are then talking about a monopoly . and it is the same word as perhaps one of your favorite board games . | what is a real life example of monopoly ? |
in the last video we saw that if we had a market with perfect competition , and if the current short-term equilibrium price is above the price the necessary or is above the price at which firms would be generating economic profit , then more and more firms would start entering . because if the economic profit is positi... | now when we do that , when we talk about one player as the only player in the market , we are not talking about perfect competition . we are then talking about a monopoly . and it is the same word as perhaps one of your favorite board games . | is monopoly a realistic condition ? |
in the last video we saw that if we had a market with perfect competition , and if the current short-term equilibrium price is above the price the necessary or is above the price at which firms would be generating economic profit , then more and more firms would start entering . because if the economic profit is positi... | now when we do that , when we talk about one player as the only player in the market , we are not talking about perfect competition . we are then talking about a monopoly . and it is the same word as perhaps one of your favorite board games . | if a 'player ' has established monopoly and has maximised his profits , then why would they risk loosing the monopoly by reducing supply to a bare minimum ? |
in the last video we saw that if we had a market with perfect competition , and if the current short-term equilibrium price is above the price the necessary or is above the price at which firms would be generating economic profit , then more and more firms would start entering . because if the economic profit is positi... | in fact , they can even go the other direction . even though they 're already making some economic profit , they might determine , hey , we can make even more economic profit if we lower the quantity offered even more . so they might even take supply out of the market . | under what circumstances a firm can not survive even the profit maximization condition holds ? |
in the last video we saw that if we had a market with perfect competition , and if the current short-term equilibrium price is above the price the necessary or is above the price at which firms would be generating economic profit , then more and more firms would start entering . because if the economic profit is positi... | well , they only have one product , one player . huge barriers to entry . no one else . | what do these terms mean : '' barriers to entry '' and `` unlimited advantage '' ? |
in the last video we saw that if we had a market with perfect competition , and if the current short-term equilibrium price is above the price the necessary or is above the price at which firms would be generating economic profit , then more and more firms would start entering . because if the economic profit is positi... | in the last video we saw that if we had a market with perfect competition , and if the current short-term equilibrium price is above the price the necessary or is above the price at which firms would be generating economic profit , then more and more firms would start entering . because if the economic profit is positi... | what is meant by mobility of factor , goods and services ? |
in the last video we saw that if we had a market with perfect competition , and if the current short-term equilibrium price is above the price the necessary or is above the price at which firms would be generating economic profit , then more and more firms would start entering . because if the economic profit is positi... | or i guess another way you can think about it , they can set their prices to whatever they want and get the corresponding quantity . but the question is , how do they set that ? how would they determine where along this curve that they would like to either set the price , or i guess you could say set the quantity by li... | is it true that monopolies may set set price and quantity of their products at any level they wish without government restrictions or regulations ? |
in the last video we saw that if we had a market with perfect competition , and if the current short-term equilibrium price is above the price the necessary or is above the price at which firms would be generating economic profit , then more and more firms would start entering . because if the economic profit is positi... | but the question is , how do they set that ? how would they determine where along this curve that they would like to either set the price , or i guess you could say set the quantity by limiting production in some way ? | does the government not do anything , such as set a quota on the minimum quantity monopolies are allowed to produce or some things like that ? |
in the last video we saw that if we had a market with perfect competition , and if the current short-term equilibrium price is above the price the necessary or is above the price at which firms would be generating economic profit , then more and more firms would start entering . because if the economic profit is positi... | and it 's at a lower equilibrium quantity . they could even do it more . they could even raise price even more . | could gas stations in a particular area get a monopoly ? |
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