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The textbook I'm currently reading (Engineering Dynamics by Paley and Kasdin) states the internal work done on a system of $N$ particles (that is, the work done by all the internal forces in the system) is as follows: $$\sum_{i=1}^N\sum_{j=1}^N\int_{C_i}\vec {F_{i, j}}\cdot d\vec{r_{i/o}}$$ where $C_i$ is the path th...
The description of charged particles in electrodynamics obeys the continuity equation, $$ \nabla \cdot \textbf{J} = -\frac{\partial \rho}{\partial t} $$ With the common physical understanding of this equation being that it describes local charge conservation. My question is whether the quantum mechanical description of...
When motorcycles accelerate quickly they do a wheelie. Where is the torque provided to lift the motorcycle?
I got a task involving a coulomb scale: Two equally charged balls (m=16g) are hanging silently on two ropes with Length $L=1.6$ m. Both ropes are installed at the same point and create relative to the vertical line an angle of $\theta=13.4$°. What is the charge of each ball in microCoulomb. https://i.stack.imgur.com/...
Please pardon my lack of proper etiquette here on this platform. I'm trying to articulate an equation of a vector that's scaling down towards zero. For example. In the movie "Honey I Shrunk the Kids". The kids were scaled down in size by some factor. If they kept scaling down further and further tending towards zero it...
Is there any study about the DMRG simulation of such kind of systems? or Each blue site is a spin, for example. Only one or several spins on each chain are coupled.
Smooth surfaces are best for effective suction cup performance. This is presumably so air can’t leak in and break the vacuum but what about the flexible cup - do we need a rough surface on the lip of the suction cup itself? If both surfaces are perfectly smooth then how can we evacuate air from the volume under the cup...
In physics, as well as in other areas of science, there are many examples of a chain reaction. The first thing that springs to mind almost Naturally, is the nuclear chain reaction: a neutron reacts with the core of a radioactive atom, after which a number of new neutrons are released. These neutrons...etc. There is the...
Everything we learn about colour in relation to matter is based on "normal" matter that has electrons around it. Absorption and emission of electromagnetic radiation is explained in terms of electrons transitioning between quantum levels with different colours being caused by the energy difference between transitions. ...
For a theory of $N_f$ massless Dirac fermions coupled to a Yang-Mills field, the usual story is that we have a $U_L(N_f)\times U_R(N_f)$ symmetry, which is then expressed as $SU_L(N_f)\times SU_R(N_f) \times U_V(1) \times U_A(1)$. However, since $U(n)\cong \left(SU(n)\times U(1)\right)/ \mathbb{Z}_n $, shouldn't the ab...
Google told me the operation frequency is 125% - 190% of the cutoff frequency. But I did not find any other material for reasoning. My question: What happens if frequency was too high?
I understand that forces are applied to charges when they are in an electric field, but what I cannot wrap my head around is how they know they are in the presence of a field. (I understand that they don't actually "know" anything). In mechanics, its relatively easy to see how forces are exchanged. For example, someone...
One of my physics teachers told me that in the formula of calculating weight i.e. $W = mg$, $m$ is not equal to 0 until and unless you're travelling close to the speed of light. She added, that the acceleration due to gravity, $g$ is also never equal to 0 because for that either mass of Earth has to be 0 or the square ...
I don't like it being defined as $\vec{r} \times \vec{mv}$ as the angular nature is not obvious in that definition. Suppose there's a single particle moving around. We choose an arbitrary origin. We define the angular momentum at time $t$ as $m|\vec{r(t)}|^2$ times its angular velocity. Angular velocity at time $t$ is ...
Solving the Schrödinger equation gives a wave function for each electron in an atom of any element. The wave functions under the atom can be squared to yield probability distribution maps, or orbitals, for electrons in that atom. Since an electron moves around the nucleus, it possesses at least kinetic energy, gravitat...
Consider a straight vortex filament as shown below. At each point, there's a point vortex of strength $\it T$. Consider that a point $P$ is there on the outermost circle of flow induced by the vortex about the origin $O$. That is the point $P$ lies in the plane containing the flow induced by the vortex at $O$. So, the ...
Let's say that a three dimensional object with continuous mass distribution is undergoing rotational motion about an axis that lies on the centre of mass. The translational velocity of the centre of mass is $\vec{0}$. I understand that the angular momentum is not zero because the direction of the $\vec{r} \times d\vec{...
When we calculate Center of mass (COM) of a hollow sphere, we assume that it's thickness is infinitesimally small, but in real world, we do not have any object with zero thickness, so how can we calculate COM of a hollow sphere with inner radius of $r$, and outer radius of $R$, which can be seen in the image.
We know that gravity is caused by the curls and warps in spacetime fabric. Does a similar explaination exist for electrostatic forces? What if there are two particles separated hundreds of kilometres apart, they will have electrostatic force between them, even though it will be negligible. How does this force "travel" ...
I read in this article (in "Independent"): An asteroid that is projected to come close to Earth later this year has a 0.41 percent chance of hitting the planet, according to Nasa data. The Center for Near-Earth Object Studies (CNEOS), from Nasa’s Jet Propulsion Laboratory, said the celestial object, known as 2018VP1, ...
Why is the angular frequency of an underdamped harmonic oscillator given by:$$\omega_1=\omega_0\sqrt{1-\zeta^2}$$
Edmund T. Whittaker published an electrodynamics theory in 1904 Proceedings of the London Mathematical Society, Vol. 1, 1904, p. 367-372. ON AN EXPRESSION OF THE ELECTROMAGNETIC FIELD DUE TO ELECTRONS BY MEANS OF TWO SCALAR POTENTIAL FUNCTIONS By E. T. Whittaker. which uses only two scalars potentials F and G to deri...
In cavity optomechanics, we see that if one of the mirrors is oscillatory and the other one is fixed,the photons are not able to shift the oscillating mirror continuously in one direction no matter how high the radiation pressure force. Why is that so? To quote wikipedia on the issue- To understand why the radiation p...
So, for a static scalar field $T(x,y,z)$, the derivative along $d\vec l$ is given by $$\frac {dT}{|d\vec l|} = |\vec \nabla T| cos\theta$$where $\theta$ is the angle between $\vec \nabla T$ and $d\vec l$ For a static vector field $\vec V (x,y,z)$, I understand that $\vec \nabla . \vec V$ and $\vec \nabla \times \vec V...
In Ryder's book on QFT page 341 we can see $$\begin{align} D_{\mu\nu}'=D_{\mu\nu}-D_{\mu\alpha}\big(k^\alpha k^\beta-g^{\alpha\beta}k^2\big)\Pi(k^2)D_{\beta\nu} \end{align}$$ and hence putting $D_{\mu\nu}=-g_{\mu\nu}/k^2,$ $$\begin{align} D'_{\mu\nu}(k)&=\frac{1}{k^2[1+\Pi(k^2)]}\Bigg(-g_{\mu\nu}-\frac{k_\mu k_\nu}{k^2...
Is the decay of a neutral rho meson into a neutral pi meson and a photon forbidden? It doesn´t look like parity conservation or charge conservation is violated but I haven´t found this decay is possible on the Internet.
In Shankar's quantum mechanics book he says the spin of electron doesn't change the energy levels of hydrogen atom(page 397, 2nd edition). How doesn't spin(being a form of angular momentum) change the energy levels? The total Hamiltonian has a piece for spin.
Suppose that the pressure inside the ship is 1 atm and that the ship is so big relative to the hole size that escaping air doesn't change the pressure much over a short time. How do I estimate the speed of the wind through it? Or, equivalently (I believe), how to compute the speed of air flow through an orifice between...
How are hot plasma simulated like fluid particles in CFD? Note: If this question is topic, i will eventually delete question but i only need an answer.
How to get the accleration of m1 in the figure using lagrangian
I recently came across the following question: The Schwarzschild metric in ingoing Eddington coordinates has the line element $$d s^{2}=-\left(1-\frac{2 M}{r}\right) d v^{2}+2 d v d r+r^{2}\left(d \theta^{2}+\sin ^{2} \theta d \phi^{2}\right)$$ What are the coordinate singularities? What are the curvature singularitie...
I was studying single slit diffraction theory from a book which said and i quote "we may assume the light source to be sufficiently far away from the slit that the photons approaching the slit can be assumed to have momentum in only the y direction" I don't understand how distance between the source and slit would chan...
When I read some scientific articles I am getting confused with the interchange being used between Torque, Couple, Moment, 'Moment Of Force'. Have I got this correct? Moment is supposed to be some action of a quantity at a distance from some point. Couple are two equal and opposite forces acting on an object , but with...
When a fluid first enters a pipe, I understand there can be a developing region as the boundary layer encompasses the flow (due to the no-slip condition). I have also heard that pressure loss in this hydrodynamic entrance region is increased due to an increased shear stress. Is there a way to calculate the pressure los...
I thought the excitation of nitrogen leads to blue lightning but I am seeing a lot of yellow lightning on the Internet https://youtu.be/nbG5g5Elq2M https://youtu.be/MRQUvjMY8wI What is the explanation?
This might be a repeated question but I couldn't find an answer already. I am told by my teacher that Coulomb's Law is valid for stationary charges. Here are the two validity criteria I am given; (i) either both the charges are at rest or (ii) one of the charge is moving and other is at rest. What if both the charges a...
I am curious about this problem due to an observation last week. A standing fan I had has its wires exposed, then it short-circuited since the neutral wire was touching the live wire directly. Then I hear a loud "pop!" with a flash of orange light. After my dad fixed it I started to wonder: what happened during the eve...
I am interested in evaluating Fourier transform of the following function analytically, $$f(t) = \sinh ^{-q}(a t) \left(1-\frac{1-a t \coth (a t)}{B}\right) $$ where $a, B, q$ are some real parameters and $B >> 1$, so one can neglect the second term inside the bracket to leading order. I tried in Mathematica and also ...
I was studying the algebric method of solving the wavefunction for a harmonic oscillator from Quantum Mechanics by Zettili and the part where he finally brings the wavefunction derived from analytic method equal to one he got from ladder operator method (Page 246) , he writes At this level, we can show that the wave f...
My main interests are biological systems, but the question is general. I was trained in computational biology, and virtually all quantitative models of biological processes I've encountered in my undergraduate studies were of probabilistic nature - Hidden Markov Models, Bayesian Networks etc. This makes sense consideri...
In which way is the Seebeck effect different for semiconductors from metals and why is it greater? What is the difference in the underlying physical principle? My knowledge so far is: Bring two materials in touch, doesn't matter which, their electrochemical potentials will align but the electrical potentials will diffe...
How exactly does a humidity sensor work? For example, how can it differentiate between a relative humidity of 30 % and 35 %? I know how a capacitance works but for me that principle is way too high level to understand a humidity sensor, I'd say. How does a sensor know that it is water inside the liquid and not just a ...
I have read that for Rayleigh scattering the photons are absorbed by the atmospheric particles then re-emitted (albeit very quickly) and the shorter wavelengths scatter better which is why the sky is blue. Am I right in saying that the sky is blue because the energy level transitions available in oxygen allow it to abs...
There's an infinite wire carrying current I on the origin along the z-axis. The question was to calculate $\int$B$\cdot$dl along the path PQ. I managed to get the correct answer by direct integration, but the solution said an equivalent path was to take the integral along the circle (RQ) and then subtract the integral ...
A similar question was asked before, but it asked for a different thing. My question here is: What is the reason for spikes in this graph? The graph initially has spikes and then shows a constant decrease. Is it related to something called magic numbers as it is seen in multiple of 4?
I hope this isn't too much of a 'why' question. Let's imagine we measure at time $t=0$ the momentum of a free non-relativistic particle with positive mass in 1D. What we find is a certain momentum $p_0$, so we can say that at time $t \geq 0 $ our particle is in the state $| \psi(t) \rangle$ defined by $$\langle x | \ps...
Take infinite space. $\mathbb{R}^3$ Then cut a sphere (a 3-ball) out of it and discard it. You now have $\mathbb{R}^3\backslash B_3$. Now take each point on the surface of the hole and identify it with it's antipodal point on $S_2$. So it is like a self-wormhole. You now have a space with a topological defect in it whi...
For instance, a symmetric change from $(-,+,+,+)$ to $(+,-,-,-)$ in a metric, what are its physical implications? If there arent, why is that?
It seems, more or less that, special relativity simply states the effect on space and time assuming that Maxwell's equations hold true everywhere, and general relativity... ...well I was thinking it was a consequence of considering gravity in light of special relativity or maxwell's equations but now it seems Einstein ...
Why are diffraction patterns similar to interference patterns? I understand interference patterns but I can't wrap my head around as to why the diffraction pattern would be similar? Does diffraction lend itself to interference? Is it not possible to have diffraction without interference at all?
Several recent things I have read say that 'quantum' materials taking advantage of entanglement, among other quantum properties, work better if very large, synthetic/artificial 'atoms' are used, which have a diameter the same size as the wavelength of the microwaves used to control them... Why do 'artificial' atoms nee...
Lets imagine that the interior of black holes are not singular, and they undergo an inflation. I know no information can escape a black hole, but the event horizon can grow in size, for instance, by accretion. Could this inflation inside make the event horizon increase in size?
Wick rotation is supposed to be a relationship between field theories with spacetime metrics of Lorentzian and Euclidean signature. I thought the definition of Wick rotation was settled, until I came across this paper — by one of the pioneers of supergravity — which proposes what appears to be an entirely different def...
I have recently hit upon an idea with which I try to make an analogy between the Coriolis force ($\mathbf F = 2m\mathbf v \times \mathbf \Omega,$) and the Lorentz force ($\mathbf F = q\,\mathbf v \times \mathbf B\,$) due to an induced magnetic field. I see that these forces are generally incapable of doing work since t...
Some background regarding my question: I'm thinking if making some sort of TEC-based ice cream maker. Considering the combined specific heat capacities, I calculated (possibly incorrectly) the value in watt hours to be slightly less than 8wh to cool 600 grams of ice cream mix (would be 1 batch) 14 degrees from (a refri...
I don't have a physics background; I assume there's some simple link to give me to answer this, but I don't know the terminology for it and so haven't been able to solve this. The use case it to avoid having my TV put divots into my IKEA KALLAX. Here's what my intuition tells me: The best shape to distribute the weigh...
I was asked the following question in my textbook: The nitrogen molecule consists of two nitrogen atoms joined by a covalent bond with length approximately 100pm. What is the approximate kinetic energy of the covalently bonded electrons? The process to solving this is to use the uncertainty relation $$\Delta p \Delta...
If a normalized array factor for an $N$-element linear antenna array (without per-element phase shifts) is calculated as $$ AF = \frac{1}{N}\sum_{m=0}^{N-1} e^{jmkd\cos\theta} $$ where: $\theta$ is the beam angle, $m$ is the element number $k$ is the wavelength-phase component ($k=2\pi/\lambda)$, $d$ is the spacing be...
I don't understand the following statement from my notes: "A fourth active neutrino is not allowed by the invisible width of the $Z$-boson to which it would contribute as much as one active neutrino, $Z \to \nu_\alpha \bar{\nu}_\alpha$." I understand that the invisible width is the uncertainty of a particle's mass and ...
Does the “amplitude” of a particle's wave packet decrease to 0 at some finite distance?
Say I have a waveguide operating on TE10 mode, as following, I need to cut a slit on the waveguide so wave can radiate. Where Should I cut the slit? I assume since TE10 mode the standing wave is between two larger plate (x- surface),therefore I need to cut on larger side?
Suppose that $|a\rangle$ is a vector in Hilbert space H. Is the projector $|a\rangle\langle a|$ "always" an operator on H? Also, what is the condition under which $|a\rangle\langle a|$ is a Hermitian operator?
I understand that the wavefunction in Quantum Mechanics is usually treated as a complex vector with one real and one imaginary component. Does it make an actual difference in terms of the answers we get, if we treat the wavefunction as having two real components instead of one real and one imaginary component, or is i...
If teleportation were to be somehow invented in the classic movie scenario (basically, enter a "magic portal" that immediately moves you to a different point in space). Ignoring some obvious problems (like the difference in local speeds between the entrance and exit "portals", one could wonder what would happen if one ...
I learned during my study that when we make a measurement of a wavefunction then the wavefunction will collapse to one of its eigenfunctions with an eigenvalue. It is also mentioned that when we instantly do the same measurement again on the same wavefunction, then we will get the same eigenvalue as the wavefunction ha...
Fundamental forces are mediated by gauge bosons. The known ones all have spin-1 but the graviton, if it actually exists, would have spin-2. How do they know this? How do the properties of the forces depend on the spin of the gauge boson which mediates it? I've read somewhere that the fact gravity is attractive only is ...
In the definition of the ground state of an atom, it is given that The ground state is one in which the electrostatic energy of attraction is minimum. This state is called the ground state of the atom. But, when the atom is in its ground state then the electron and the nucleus will be closest as compared to when the...
If there are 8 gluons, and 6 of them can be represented as a color/anticolor pair (red/antiblue for example), that leaves 2 "other" gluons. How do these two gluons differ from each other? What happens when two quarks exchange one of these gluons? What happens when two quarks exchange the other of these gluons? Are thes...
Consider a situation with two blocks with a spring between them vertically. I am interested in the compression required in order to lift the system of the ground? What is the force required to do this? I've drawn what I think the forces will act like, but don't know how to find out how much force is required in order ...
$$\large{I_1\dot{\omega}_1+(I_3-I_2)\omega_2\omega_3=M_1}$$ $$\large{I_2\dot{\omega}_2+(I_1-I_3)\omega_3\omega_1=M_2}$$ $$\large{I_3\dot{\omega}_3+(I_2-I_1)\omega_1\omega_2=M_3}$$ In Taylor's Classical Mechanics, it is said that the equations are generally difficult to use because the components $M_1,M_2$ and $M_3$ of ...
why we detect an increment in the number of events of the reactions for the energy of resonance particles? I read that cross section of this new unstable particle must be added to the cross section of the target particle but i cannot understand the reason. A little example of concepts i cannot understand, we have a pr...
We know that for a gravitational field calculation $E = \frac{GM}{r^2}$ we consider a test mass, i.e. a small mass, but how does a big mass actually affect the gravitational field.
So there is Pauling electronegativity scale, but thous are constants based on experiments, right? Another way is Allred-Rochow method, but it has rumors being a bit imprecise comparing to real measurements. Are there any other good methods where I can calculate electronegativity given electron configuration?
I read that electrons being emitted from a Cs plate when irradiated with photons with energy greater than work function of Cs, are used in a double slit experiment. But, should they not have varying initial phases, such that visible interference can't occur due to constant variation of intensity at any point?
In Rigid body rotation, we need only 3 parameters to make a body rotate in any orientation. So to define a rotation matrix in 3d space we only need 3 parameters and we must have 6 constraint equation (6+3=9 no of elements in rotation matrix) My doubt is if orthogonality conditions R.Transpose(R)=I must be satisfied for...
When atoms bind together, their total energy is less than each individual's energy. When planets come together, their total energy is also less (i.e. nature of attractive force). The mass of each stays the same before and after the binding. However, their total energy decreases. Does this mean that when planets come t...
According to the kinetic theorem of gases, the internal energy of an ideal gas is solely dependent on the temperature of a gas. In the free expansion of a gas, it is said that the internal energy change in the gas is zero because the temperature is constant. Let us consider a piston compressing a gas. Ultimately the re...
I have read lots of thing on probability in QM and the different ways of intending it. Now, I am wondering how physicists intend probability in classical physics. To be more specific, I have read some articles about the fact that probability in classical physics is seen by physicists as bayesian probability. I am not s...
I am trying to find the Glauber P function for a superposition of Coherent States: $$\psi=\frac{1}{\sqrt{2}}(|\beta\rangle +|-\beta\rangle)$$ where $\beta$ is real. The P function is defined as: $$P(\alpha)=\frac{e^{|\alpha|^2}}{\pi^2}\int d^2u \langle-u|\rho|u\rangle e^{|u|^2}e^{\alpha u^*-\alpha^*u}$$ Using the ortho...
What I Know: $$ \vec F = -k \vec x $$ where the negative sign indicates the Force acts in the opposite direction to the displacement. If we were to take the integral so... $$\int_{x_i}^{x_f} Fdx = -\Delta U$$ What would the negative sign in this instance represent? From my understanding, we cannot produce negative ener...
I am initiating my learning on QFT and my question might be really basic, but I am having difficulties finding an answer, I would appreciate any help to find this in the literature. Here is my question: If all dimensions are independent and co-exist (here and now). If humans are not able to see all dimensions, but we m...
What if negative mass is a property of space-time itself? We know that dark energy works against gravity and is currently expanding universe, while this expansion is increasing. Can this be because the hypothesized negative mass repels the positive mass, which causes a repulsive gravitational force. Please give your o...
I'm wondering how important floating-point precision is in numerical simulations of molecular dynamics in biology. From what I understand, molecular dynamics programs like NAMD use 32-bit floats to represent the various numbers involved in simulations (or at least, this mailing-list entry suggests that this is the cas...
While studying the corrections of fine structure in the hydrogen atom my book tries to justify the spin-orbit term with some arguments about magnetic energy an spin. I'm fine with the calculations but I don't understand where his starting point comes from. It says that the magnetic field generated by an electron moving...
Assume we have a step potential $$ V(x)=\left\{\begin{array}{ll} 0, & x<0 \\ V_{0}, & x \geq 0 \end{array}\right. $$ and we fire particles from a distance $s$ towards the barrier from the left. Using the Schrödinger equation we get the solutions in the two regions as: \begin{align} \varphi_{1} & =A e^{i p_{1} x / \hbar...
I know the theory of electromagnetics in BSC-MSC level, e.g.: as like in these physics books: Alvin Hudson Rex Nelson UNIVERSITY PHYSICS David J. Griffiths INTRODUCTION TO ELECTRODYNAMICS But now I would like to find an electromagnetic text book for electrical engineers in English. The following books in German languag...
For testing purpose, I'd need a material that could change of color after being exposed to UV for a period of time (let's say, few minutes). Do you know if such a material exists or is it better to use a device to measure the UV at a certain location? Thanks in advance for you answers and have a great day! Adrien
The Lagrangian for a spherical pendulum of length $l$ is $$ L = (1/2) m l^2 (\dot{\theta}^2 + sin^2(\theta) \dot{\phi}^2) + mg l cos \theta $$ Landau and Lifshitz state, "The coordinate $\phi$ is cyclic, and hence the generalized momentum $p_\phi$, which is the same as the z-component of angular momentum, is conserved...
I am have written a Metropolis-Hastings algorithm and am currently trying to compare it to the analytical results for the 2D Ising model. The free energy seems reasonable but the heat capacity I'm getting is way off. I am using the equation $C_{v}=\frac{\beta}{T}[\left<E^{2}\right>-\left<E\right>^{2}]$. Using $\beta=1$...
Recently, I got caught in the rain while riding my road bike. Being wet and miserable made me ponder the following: The general wisdom is that wet roads are more slippery, thus the rider should be more careful with braking and cornering. If there is less friction between the road and the tire, it should take less energ...
I am studying nonlinear optics, specifically the wave equation of nonlinear optical media. During the derivation I came across a point where the divergence of electric field was zero for a linear isotropic medium. I couldn't understand the reason behind it.
I am reading the paper "ABC of instantons" and meet some problems at section 8. I simplify this problem a little bit as follows. First, we have a Euclidean path integral like \begin{equation} Z=\int \mathcal{D}A\; {\rm e}^{-S},~~~S=\int d^4x \mathcal{L}_0(A^{a}_{\mu}) \end{equation} An instanton is a solution of equati...
Is it because they eat more than they eject? Or something else? Edit ------- I mean black holes which have just started forming from stellar collapse. Should had mentioned this. Edit 2 ----- When you have a ball of neutrons which is compressed to the maximum extent physically possible during stellar collapse, the spati...
I'm having a hard time getting the difference between the two. In Euler's equations of rotating bodies for example, we have: $$ \mathbf{\dot{L}}+\mathbf{\omega} \times \mathbf{L} = \mathbf{\Gamma},$$ where the torque $\mathbf{\Gamma}$ is (please correct me if I'm mistaken) in the space (inertial) reference frame, but e...
I read on a website that if the sun is removed from its position then it would take some time for the earth to feel the effect i.e. flying off tangentially from the orbit. In a slightly different case, suppose I have a rope with a bob at one of its ends and the other end is in my hand. I can hold the rope tightly becau...
And also while analysing Earth's spinning motion about its center? Do we have to care about the forces from the giant Black Hole at the center of Milky way? I guess we would have to take the Black Hole force into account, as it is an external force on every single particle of the system? Switching to the CoM frame may ...
The Python poliastro package documentation states that, when propagating from position and velocity vectors, the orbit's reference frame will be "one pseudo-inertial frame around the attractor," which in the case of earth-orbiting objects, means some form of ECI. However, I want to make sure I am matching up coordinat...
When we apply a voltage across a metallic conductor, the current starts to flow almost instantaneously. But when a temperature difference is established across the same conductor, the flow of heat is much slower. It takes larger time for the heat to reach from one end to the other than the current. Why is this so?
I have been learning mathematics and now I'm trying to learn physics as well. I have some difficulties: (a) There are lots of approximations in physics, and that's very different from mathematics. How should one treat these approximations? It seems to me I can only try to memorize them, since I haven’t figured out a w...
Question: A monkey of mass $m$ moves up on a massless string so as to just lift a block of mass $M$. After some time the monkey stops moving with respect to the string. Find the magnitude of change in the monkey's acceleration. Answer: $\Delta a = \dfrac{Mg(M-m)}{m(M+m)}$ I can't even understand how to begin solving th...