In introductory mechanics, the momentum of a particle is its mass times its velocity. In electrodynamics, the momentum of a field is proportional to the cross-product of the electric field with the magnetic field. In special relativity, momentum is generalized to four-momentum.

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How to derive the velocity in the double ball drop problem?

The double ball drop problem is as follows: A ball of mass $m$ is placed on top of a ball of mass $M$ (where $m < M$), and the balls are dropped simultaneously from some height $h$. When the ...
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616 views

Impulse from absorbing a photon? Is there an increase in rest mass?

I'm going through A P French's special relativity. In one chapter (6) the following is set up: Suppose that a stationary particle of mass $M_0$ is struck by a photon of energy $Q$, which is ...
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812 views

Conservation of linear and angular momentum

Suppose I have two rigid bodies A and B and they are connected by a spring which is attached off-center (thus possibly causing torques). Due to the spring a force $f$ acts on A and a force $-f$ acts ...
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Confusion between the de Broglie wavelength of a particle and wave packets

So I learned that the de Broglie wavelength of a particle, $\lambda = \frac{h}{p}$, where h is Planck's constant and p is the momentum of the particle. I also learned that a quantum mechanics ...
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369 views

What is the result of a classical collision between THREE point particles at the same precise instant?

Classical Mechanics is said to be deterministic, a statement that nearly always is followed by that quote from Laplace, something like If at one time, one knew the positions and velocities of all ...
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Tricky spring on a surface question

I have this relative simple-looking question that I haven't been able to solve for hours now, it's one of those questions that just drive you nuts if you don't know how to do it. This is the scenario: ...
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Why do we need the quantity momentum?

Why do we need the quantity Momentum in physics when we have the quantities like Force and Energy? Isn't it possible to substitute the usage of Momentum with equivalent of Force and Energy?
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Would a sneeze by a cosmonaut in a spacesuit affect his movement?

Naive question; feel free to shoot me down It is a truism that any motion in space would continue indefinitely unless it is opposed by an external force. If a cosmonaut were to sneeze within his/her ...
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Uncertainty Principle for a Totally Localized Particle

If a particle is totally localized at $x=0$, its wave function $\Psi(x,t)$ should be a Dirac delta function $\delta(x)$. Accordingly, its Fourier transform $\Phi(p,t)$ would be a constant for all $p$, ...
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Complex conjugate of momentum operator

Consider momentum operator representation in position space. $$\hat{p}=-i\frac{\partial}{\partial x} \,\ \text{and its eigen functions are } e^{ipx} \,\text{and} \,\ e^{-ipx}.$$ ...
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Does the canonical commutation relation fix the form of the momentum operator?

For one dimensional quantum mechanics $$[\hat{x},\hat{p}]=i\hbar $$ Does this fix univocally the form of the $\hat{p}$ operator? My bet is no because $\hat{p}$ actually depends if we are on ...
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467 views

How does the momentum operator act on state kets?

I have been going through some problems in Sakurai's Modern QM and at one point have to calculate $\langle \alpha|\hat{p}|\alpha\rangle$ where all we know about the state $|\alpha\rangle$ is that ...
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Why is the “canonical momentum” for the Dirac equation not defined in terms of the “gauge covariant derivative”?

The canonical momentum is always used to add an EM field to the Schrödinger/Pauli/Dirac equations. Why does one not use the gauge covariant derivative? As far as I can see, the difference is a factor ...
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Hammer vs large mass on nail

Why is a hammer more effective in driving a nail than a large mass resting over the nail ? I know this has to do with momentum, but cant figure it out.
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Directional derivatives in the multivariable Taylor expansion of the translation operator

Let $T_\epsilon=e^{i \mathbf{\epsilon} P/ \hbar}$ an operator. Show that $T_\epsilon\Psi(\mathbf r)=\Psi(\mathbf r + \mathbf \epsilon)$. Where $P=-i\hbar \nabla$. Here's what I've gotten: ...
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Intuitive explanation of why momentum is the Fourier transform variable of position?

Does anyone have a (semi-)intuitive explanation of why momentum is the Fourier transform variable of position? (By semi-intuitive I mean, I already have intuition on Fourier transform between ...
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Which will stop first a heavier car or a lighter car?

If the friction from brakes, wind resistance and all such factors remain constat, which will stop first? A heavier car or a lighter car? How will the momentum of the car and graviational pull on a ...
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325 views

Applications of recoil principle in classical physics

Are there any interesting, important or (for the non physicist) astonishing examples where the recoil principle (as special case of conservation of linear momentum) is applied beside rockets and guns? ...
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Conservation of Energy and Momentum Regarding Forces - clarification needed

The other day, my teacher stated something along the lines of, "Conservation of momentum is not violated by the actions of internal forces, but the conservation of energy is violated. Energy is ...
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Usefullness of an only qualitative understanding of momentum?

A few days ago I had a discussion with a friend who wants to become a physics teacher (in Germany). He told me that from a pedagogical/didactial point of view it seems to be a good idea to introduce ...
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234 views

Uncertainly Principle in orthogonal directions

The Heisenberg Principle states that for each direction, $\Delta x\cdot \Delta p_x \ge \hbar , \Delta y\cdot \Delta p_y \ge \hbar$ and $\Delta z\cdot \Delta p_z \ge \hbar$. But, can anything be said ...
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136 views

Do $x$ and $Q^2$ associate with particular directions in the infinite momentum frame?

In deep inelastic scattering, you describe a collision using the variables $Q^2 = -q^2$ (probe virtuality) and $x = Q^2/2p\cdot q$ (Bjorken x, parton momentum fraction). Now, I seem to remember ...
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Different results to a basic question ( Newton's law and perservation of momentum)

Trolley with mass of $m_0=1 \ kg$ is moving without friction on the railway track. It is raining so there is a constant mass flow of water $\Phi_m=0.1\ kg/s$. Constant force $F=0.1 \ N$ is ...
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When I move my arm forward in vacuum, will my body move backward?

Let's say I stay at point $x=0$ in vacuum. When I move my arm forward such that it will have a positive $x$ position (say $x=5$) will the rest of my body move backward such that it will have a ...
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Can it require different amounts of energy to generate the same impulse?

According to impulse principle the impulse is the same as the change in the object's momentum: $\bar I = \delta p$ Because the momentum can be calculated like this: $\bar p = m\bar v$. If we solve ...
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What is the most general expression for the coordinate representation of momentum operator?

I have a question about deriving the coordinate representation of momentum operator from the commutation relation, $[x,p]= i$. One derivation (ref W. Greiner's Quantum Mechanics: An Introduction, 4th ...
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248 views

Firing machine question

Suppose we have a firing machine on a frictionless surface at point $x=0$. It fires a bullet of mass $m$ every $T$ seconds. Each bullet has the same constant velocity $v_0$. There's a body of mass ...
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703 views

Use of Operators in Quantum Mechanics

I understand the form of operators in use for quantum mechanics such as the momentum operator: $$\hat{\text{P}}=-ih\frac{d}{dx}$$ My question is in what ways can I use it and what am I getting back? ...
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646 views

How do you combine two rigid bodies into one?

With respect to some fixed frame of reference, given the inertial tensors, positions, orientations, and angular and linear velocities of two rigid bodies, how do you combine them to make a single ...
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Why is momentum conserved in an inelastic collision and kinetic energy is not conserved?

We know that in an inelastic collision that total momentum of the system before collision equals the total momentum after collision. But total kinetic energy before collision is not equal to total ...
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Conservation of momentum and energy in an explosion

One simple problem is physics is to determine the mechanical energy difference after an explosion. To do this, you must assume that momentum is conserved because in a explosion you have internal ...
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141 views

Why doesn't a wall move when you push it if there's space behind it?

In the first screen you can see that if a person were to push a wall within a typical household the wall would not move while keeping themselves tractioned to the floor. If you push hard and do not ...
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Is momentum conservation for the classical Schrödinger equation due to non-relativistic or due to some more exotic invariance?

I had no problem appliying the Neothers theorem for translations to the non-relativistic Schrödinger equation $\mathrm i\hbar\frac{\partial}{\partial t}\psi(\mathbf{r},t) \;=\; \left(- ...
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Use the relative velocity formula to find v2f in terms of v1f?

Q: A $0.150\text{ kg}$ glider is moving to the right ($+x$) on a frictionless, horizontal air track with a speed of $0.80\text{ m/s}$. It has an elastic collision with a $0.300\text{ kg}$ ...
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Conservation of momentum in collision of two bodies

Suppose we have some ramp on wheels of mass $M$, standing on a frictionless surface. A cart of mass $m$ moves with a certain velocity $v$ towards the ramp. The cart moves up the ramp ...
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Why does Energy-Momentum have a special case?

I was reading Energy-momentum, and I came across this simplified equation: $$E^2 = (mc^2)^2 + (pc)^2$$ where $m$ is the mass and $p$ is momentum of the object. That said, the equation is pretty ...
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Deriving $F = ma$ - Newton's Second Law of Motion

Context: In my textbook it is given: 'momentum' short for 'linear momentum': Mass = $m$, momentum is $p=mv$. In time $\Delta t$, momentum changes by $\Delta p$, the rate of change of momentum is: ...
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Newton's 3rd Law: How can I break things?

If I punch a wooden board hard enough and it breaks in two, has the board still exerted a force of equal magnitude on my fist? When the board breaks in two due to my force, the halves have a ...
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How can momentum but not energy be conserved in an inelastic collision?

In inelastic collisions, kinetic energy changes, so the velocities of the objects also change. So how is momentum conserved in inelastic collisions?
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Energy definition in special relativity

I'm going through the early homework assignments for my special relativity course and I've got myself a little confused about energy. I've got a basic understanding of what the 4-momentum is, having ...
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Why do safety helmets have a softer inner layer nearer the head?

I know that when an object collides onto the helmet, it causes an inelastic collision so that energy is absorbed by the structure of the helmet, so what exactly does the softer inner layer do? Does it ...
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Does constraint for speed of Electric and magnetic fields violates Conservation of momentum or Newton's third law?

I'm just a beginner so bear with me. Consider two frames at rest wrt to each other separated by distance enough for light to take a minute or so. At a given instant we create two large dipoles by some ...
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Total momentum of the Universe

What is the total momentum of the whole Universe in reference to the point in space where the Big Bang took place? According to my reasoning (and a bit elementary knowledge) it should be exactly ...
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108 views

Impulse, relative velocties

Why is (m)(v)=Impulse or as they put it here, Vs = I/Ms? Shouldn't (m)(v) be equal to momentum, not I? I don't understand why that is the solution. I was trying to solve for relative velocities, ...
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478 views

Conservation of Energy in Different Frames of Reference

Say I have a bucket of fuel that can produce 150J of energy by combustion. No matter what frame of reference an observer or the bucket of fuel is in, since the configuration of molecules stay the ...
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Derivative of a Position Eigenket

I was flicking through Zettili's book on quantum mechanics and came across a 'derivation' of the momentum operator in the position representation on page 126. The author derived that ...
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Conservation of Momentum/Energy collision Problem

I'm working on a physics problem in preparation for the MCAT and there's this particular problem that's troubling me. I don't know if it's a bad question or if I'm not understanding some sort of ...
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Momentum-Representations in Quantum Mechanics

Why do we get information about position and momentum when we go to different representations. Why is momentum, which was related to time derivative of position in classical physics, now in QM just a ...
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Probability of measuring momentum [closed]

Suppose we have this wavefunction: $$ \psi = A \left( cos(kx) + cos (2kx) \right) $$ I have to find the possible results of measurement of momentum and their probabilities. Attempt For a momentum ...
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679 views

Can the velocity of the center of mass of two spheres change after a collision?

I'm curious as to whether or not the velocity of the center of mass of a system comprised of two spheres can change after the two spheres collide. Looking at the equation for the velocity of the ...