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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What happens with a tunneling particle when its momentum is imaginary in QM?

In classical mechanics the motion of a particle is bounded if it is trapped in a potential well. In quantum mechanics this is no longer the case and there is a non zero probability of the particle to ...
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1answer
105 views

Energy/Momentum required to deflect earth from its orbit

This question occurred to me when thinking about the firepower people have on earth. How hard is it to change the characteristics of the orbit of the earth when an explosion happens on its surface, ...
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Calculating angular velocity after collision

Suppose I have a disc which doesn't move, just rotate around the axis going through its centre of mass perpendicular to its surface. The disk has a stick perpendicular to its surface at the edge. I ...
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3answers
1k views

Steady isothermal flow of an ideal gas

So I have a steady isothermal flow of an ideal gas through a smooth duct (no frictional losses) and need to compute the mass flow rate (per unit area) as a function of pressures at any two different ...
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2answers
1k views

Conservation of linear momentum magnitude along a trajectory

I was once criticized for "taking angular momentum as momentum going in a circle". I was loosely trying to state, in classical mechanics, that in using conservation of momentum, one can switch between ...
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1answer
774 views

Quantum mechanical analogue of conjugate momentum

In classical mechanics, we define the concept of canonical momentum conjugate to a given generalised position coordinate. This quantity is the partial derivative of the Lagrangian of the system, with ...
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663 views

Single photon's effect on conservation of momentum?

When your looking at basic Compton theory you find that if you shoot a stream of photons at a particle (usually atoms or electrons), then you have the basic laws of conservation of momentum. The ...
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397 views

Displacement with zero velocity

I know that we can rotate a deformable object using internal forces only in space. Thus we can cause an angular displacement without the use of any external forces. The following youtube video shows ...
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1answer
334 views

Conservation of momentum with MOND

Assuming as true the phenomenological MOND law for low accelerations ($< 10^{-10} m s^{-2} = a_0$), and considering a small mass $m$ attached to a larger mass $M$ by a faint spring (let's think of ...
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1answer
245 views

Mass Shell in Light Cone Coordinates

I'm reading Zweibach's introduction to string theory, and don't understand one of his claims. He defined the mass shell to be the set of points in momentum space s.t. $p^2+m^2 = 0$. Then the physical ...
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3answers
241 views

Should any theory of physics respect the principle of conservation of angular momentum or linear momentum?

Is it possible that a theory that can describe the universe at the planck scale can violate things that we now consider fundamental in nature?For example can it violate rotational and translational ...
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1answer
53 views

Simple frame of reference problem (conservation of momentum?)

I'm having trouble wrapping my head around a particular concept. Suppose we have a machine that fires balls of speed $u$ at some mass rate $\sigma$ (of units $\frac{kg}{s}$) directly at a car of mass ...
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3answers
165 views

Derivation of $E=pc$ for a massless particle?

In classical mechanics, massless particles don't exist because for $m=0$, $p=0$. The relativistic relation between energy, mass and spatial momentum is: $E^2= (pc)^2 + (mc^2)^2$ . So it is said that ...
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1answer
167 views

Relativistic Lorentz Force with constant, perpendiuclar, and uniform E and B fields

I am trying to solve the following problem from the Fundamentals of Plasma Physics by Bittencourt (Problem 2.7): Analyze the motion of a relativistic charged particle in the presence of crossed ...
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1answer
140 views

What's the physical meaning of change in momentum vector?

If I there is a initial momentum of 10Ns upwards, and final momentum of 10Ns to the right, I can find the difference in momentum by drawing a triangle and finding the resultant vector. But, how is ...
2
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1answer
42 views

How to pull out the momentum operator?

In the equation (1.7.17), how does operator $p$ get out of the bracket without any operation though $<a | $, $| x'>$ are function of $x'$? How to prove this?
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1answer
155 views

Finding final velocity in inelastic collision [closed]

Information: In a shipping company distribution center, an open cart of mass 49.0-kg is rolling to the left at a speed of 5.40-m/s (see the figure). You can ...
2
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2answers
181 views

Problem on electromagnetic induction and Newtonian physics

Please imagine a solenoidal toroid (i.e. a donut shaped inductor) powered by an AC voltage source. It creates a changing magnetic field which is confined to the interior of the toroid (i.e. within the ...
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1answer
149 views

Doubt regarding stress-energy tensor definition

I'm having some trouble understanding the following definition of the stress energy tensor: $T^{\mu\nu}$ is the flux of four-momentum $p^{\mu}$ across a surface of constant $x^{\nu}$. Here's an ...
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2answers
225 views

Does constant velocity of center of mass imply linear momentum is conserved?

I know that if momentum is conserved for a system, you can derive that the velocity of the center of mass of that system is constant. I was wondering if the second condition also implies the first: if ...
2
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1answer
361 views

Total Momentum From a Standing Electromagnetic Wave

How does one show the momentum imparted to a perfect conducting resonance cavity (boundary) of any shape by a classical standing electromagnetic wave inside is zero? It should be by conservation of ...
2
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1answer
53 views

Swinging onto a Hill

I was just watching the movie "Frozen" (not the Disney one), and they were trapped in a ski lift 50 feet off the ground. They had to jump. My question is, when they jump, should they swing on the ...
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4answers
191 views

Losing mass in space

So I came across a question while studying laws of motion. Roughly, this is how it goes: There are two astronauts in a space shuttle, who together have mass 200 kg. If by doing exercise, they manage ...
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89 views

Relativistic fomulae for energy and momentum?

I know that the relativistic formulae for energy and momentum are: $E = \gamma mc^2$ and $\textbf{p} = \gamma m\textbf{v}$; Can we derive these formulae? If yes, where from?
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359 views

Symmetries of a Uniform Magnetic Field

Simple question. A system with a uniform electric field everywhere in space has translational invariance in the directions perpendicular to the electric field but no translational invariance parallel ...
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2answers
5k views

Conservation of momentum when friction is present

Conservation of momentum applies when net force is zero. Suppose that there is a system of a canon and a canonball. Total momentum of the system is zero before canonball is fired. Now canonball is ...
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1answer
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Proof that the momentum operator is Hermitian

I am trying to prove that the momentum $p_x$ operator is Hermitian, my approach is the following $$<p_x>~=~\int \Psi^*(\vec{r},t)[-ih\frac{\partial}{\partial x}]\Psi(\vec{r},t)\, d^3r.$$ I try ...
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1answer
4k views

Heavy vs Light Particle Ideal Gases

Assume there are two ideal gases. The first is made of a light particle, and the second is made of a heavy particle. The two are of the same amount, in the same volume container, and at the same ...
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3answers
569 views

Two dimensional elastic collisions with varying angle of incident

If in an elastic collision I know all initial values and that mass for each object remains constant throughout the collision (but different from one another) how can I determine their final velocity ...
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1answer
661 views

Fundamental properties of motion

The first paragraph of the Wikipedia article on the angular momentum operator states that In both classical and quantum mechanical systems, angular momentum (together with linear momentum and ...
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2answers
750 views

Movement of man and ladder and their center of mass

Suppose there is a massless frictionless pulley. A rope over it carries a mass $M$ and on other side carries a ladder of mass $(M-m)$ and a man on that ladder, of mass $m$. Now the man starts ...
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1answer
421 views

Relativistic kinematics of particle decay

Suppose a particle decays to three other particles. The masses of all particles are assumed to be known and we work in the rest frame of the parent particle. So there are 12 parameters for this ...
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1answer
3k views

Finding force exerted in an Inelastic Collision

I did a lab today in Physics in which we launched ball from a spring loaded cannon directly into a pendulum that captured the ball, held it, and swung upwards with it (representing a totally inelastic ...
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1answer
618 views

momentum conservation question involving a rocket and a spaceship [closed]

With the engines off a space ship is cruising at a velocity of 230m.s It fires a rocket straight ahead at the enememy vessel. The mass of the rocket is 1300kg and the mas of the ship (not including ...
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1answer
1k views

Converting angular velocity to linear velocity through friction

A very basic question here; it's related to this one, but not quite the same. If a rotating rigid body (a sphere for the sake of discussion) with mass $m$, radius $r$ and inertial tensor $I$ has ...
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962 views

What is the linear momentum of an EM wave in a medium?

In free space, the linear momentum density of an EM wave is given by the Poynting vector $\vec S$ over the speed of light squared, $\vec g=\frac{\vec S}{c^2}$. In a medium, $S$ is generally not ...
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1answer
45 views

How can you find the impact necessary to change the direction of Earth's spin?

If an object the mass of the moon was to hit earth's surface at an angle that would be in the opposite direction of earth's spin, how can you find how much momentum the object needs to cause earth to ...
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What happens to Newton's Third Law during the reflection of a pulse from a free end?

Well, it is known that a pulse gets inverted when it gets reflected from a fixed support while the polarity of the pulse remains same when the incident pulse gets reflected from a free end. However, ...
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Momentum Twistor variables and non-planar theory

I know that the use of twistur-momentum variables makes manifest the arising of certain poles in scattering amplitudes: if the sum of external momenta $P_I = p_i + p_{i+1} + ... + p_j$ is going ...
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1answer
62 views

Is $E = p^0$ in non-inertial frames?

In special relativity the energy of a particle is the 0-component of the 4-momentum. However, is this still true in non-inertial frames, and in particular in non-freely-falling frames in general ...
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307 views

Portal 2 physics - one moving portal [closed]

A problem is posted and solved so many times on 9gag - till yet no good answer. The problem: you have two portals (one moving and one still standing). The one moving reach a still standing cube: what ...
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59 views

Is my expansion of the state $| x \rangle$ correct? [duplicate]

In my quantum mechanics textbook it says that the relation between the basis $|x\rangle$ and $|p\rangle$ is given by: $\langle p | x \rangle = \Large \frac{e^{-ip x/ \hbar}}{\sqrt{2\pi \hbar}} \, .$ ...
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Derivative of the action integral [closed]

I need to find the partial derivative of the action $S$ with respect to the generalized coordinate $q(t_f)$ and according to my textbook, it should equal the generalized momentum $p(t_f)$. I ...
2
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0answers
63 views

Finding the momentum of a muon in $\pi\to\mu\nu_\mu$ [closed]

The $\pi$-meson's mass is 139.57 MeV, and it decays into a muon and a neutrino. The muon has a mass of 105.4 5MeV, and a proper lifetime of $2.197 \times 10^{-6}$. The neutrino can be treated as ...
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Equating $\frac{dp}{dt}$ and $F$ at a hydraulic jump?

A journal I am reading about circular hydraulic jumps provides the equation and I quote: $H$= Depth after hydraulic jump, $h$= depth before hydraulic jump, $V$= velocity after hydraulic jump, $v$= ...
2
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1answer
151 views

The norm of the vector sum of two 4-momentum vectors before and after pair production

Two photons traveling along the x-axis (in a lab frame of reference) of different frequencies are about to collide. Their 4-momentum vectors are (h$\nu_1$/c , h$\nu_1$/c , 0, 0) and (h$\nu_2$/c , ...
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What exactly is NASA's proposed mechanism for “propellantless” “EM Drive” propulsion? [duplicate]

Of course, this question runs perilously close to this site's prohibition against discussing non-mainstream physics. However, the accepted answer in meta about what is acceptable and what is not ...
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1answer
168 views

Is my proof of the thought experiment that Walter Lewin proposed in lecture 16 valid? [closed]

A tennis ball bounces off a wall elastically. The momentum of the wall changes, but the kinetic energy of the wall remains zero. How is that possible? Walter Lewin Lecture 16 - Ball bouncing on ...
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Can an electron borrow momentum from its field?

Let us consider a charged particle moving with uniform velocity $v$. We know that the EM field due to it has some momentum too. If the mass of the particle is $M$, then the momentum of the particle is ...
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1answer
65 views

Does the spatial momentum of the ground state of a Poincare symmetric QFT vanish?

Consider a flat space QFT, the Lagrangian (in general interacting) has Poincare symmetry, and $\lvert\Omega\rangle$ is the ground state (or just merely no insertion at the far boundaries, from ...