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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Momentum flux through cylinder wall

A fluid flows through a hovercraft, is bended and the freejet has a certain velocity $c$ with which it flows after exiting the hovercraft / beeing bended. There's a pressure difference between under ...
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1answer
131 views

Is conservation of momentum and energy valid for non-inertial frames?

Conservation laws of momentum and energy are said to be the most basic principles of physics. Are they also valid for non-inertial frames, and in what way?
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2answers
84 views

If I throw or kick a ball, how much will the Earth move in the opposite direction?

I understand that for momentum to be conserved, if I throw a tennis ball (or kick a football) the Earth must move in the opposite direction to the ball. Obviously this is an infinitesimally small ...
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1answer
48 views

Collision/Crumpling problem possible solution mistake

This question is from Physics for scientist and engineers , Ohanian . Two automobiles of 540 and 1400 kg collide head-on while moving at 80 kmh in opposite directions. After the collision the ...
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0answers
50 views

Integrals of motion for a free particle

I'm struggling to understand the argument on p. 13 in Landau and Lifshitz that for a system with $N$ degrees of freedom there must be $2N-1$ integrals of motion. In particular, I can't understand ...
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1answer
135 views

Mathematical proof of an electron can't absorb a photon [duplicate]

How can we mathematically prove that a free electron can't absorb a photon totally?
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1answer
61 views

Newton's 2nd Law with Dirac Delta, as a way to derive the Ideal Gas Law

I'm trying to derive the ideal gas law from first principles, namely that a particle bouncing off a wall will exert a force on the wall. Newton's second law $F=\frac{dp}{dt}$ relates the force an ...
2
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1answer
167 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 , -h$\...
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3answers
416 views

Momentum of transverse waves on a string

In general, if a wave carries energy density $u$ with velocity $v$, it also carries momentum density $u/v$. I've seen this explicitly shown for electromagnetic waves and (longitudinal) sound waves. ...
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3answers
58 views

Can internal forces bring any change in momentum of the system?

Imagine a rectangular box placed at the tip of an iceberg; the box contains a man who can freely walk/jump/rotate inside the box. The man walks up to one of the corners of the box and starts jumping. ...
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2answers
60 views

Heisenberg EOM for $\langle x \rangle$ in momentum eigenstate - where is my error?

Equation of motion for expectation value of a quantum particle in a momentum eigenstate: $$\frac{d}{dt} \langle x \rangle = \frac{1}{i h} \langle [x,H] \rangle$$ and since it's in a momentum ...
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3answers
2k views

What are some phenomena that can not be described without the help of Newton's third law of motion? [closed]

What are some phenomena that can not be described without the help of Newton's third law of motion? All the phenomena I can think of can be explained with the help of Newton's first law or second law. ...
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3answers
4k views

Matrix elements of momentum operator in position representation

I have two related questions on the representation of the momentum operator in the position basis. The action of the momentum operator on a wave function is to derive it: $$\hat{p} \psi(x)=-i\hbar\...
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2answers
287 views

Deriving the expectation of $[\hat X,\hat H]$

For a free particle of mass $m$, with Hamiltonian $$\hat{H} = \frac {\hat{P}^2} {2m},$$ where $$\hat{P} = -i \hbar \frac{\partial} {\partial x}.$$ The commutative relation is given by $$[\hat{X}, \...
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3answers
4k views

What's wrong with this derivation that $i\hbar = 0$?

Let $\hat{x} = x$ and $\hat{p} = -i \hbar \frac {\partial} {\partial x}$ be the position and momentum operators, respectively, and $|\psi_p\rangle$ be the eigenfunction of $\hat{p}$ and therefore $$\...
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8answers
3k views

Can we explain Newton's first law mathematically?

At constant speed there is no acceleration. $(f'(x)=v'=0=a)$ .If $a=0$ then $F=ma=0$ and therefore no force acts on the object so the object will continue in the same direction, if any. This is only ...
2
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2answers
6k views

What is the Momentum Operator?

I know the equation for the momentum operator, but what exactly is the momentum operator? It's bizarre to me that taking the derivative of the wave function, which is an operator, should return ...
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1answer
130 views

What will happen to the center of mass of the human body when a person carries a weight with one hand?

What will happen to the center of mass of the human body when a person carries a weight with one hand a briefcase for example. Wouldn't the center of mass move horizontally towards the side carrying ...
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1answer
50 views

Impulse of two different objects

I was running over a question, A collision occurs between particles A and B which are moving in opposite directions in the same straight line. The impulse on each particle in the collision is 2N.s, ...
2
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2answers
96 views

Newton's Cradle: why does it stay symmetric? [duplicate]

How is it that always the same number of balls leave at the other end in Newton's cradle. I understand that the momentum needs to be conserved, but as momentum is defined as p=m*v couldn't you have a ...
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1answer
24 views

Probability to measure momentum of a certain range (eigenfunctions and such)

At a certain point in time a particle of mass $m$ has the corresponding function (function of $x$) $$\psi(x)=\begin{cases}Nx \exp[-bx]~~&\text{for}& x\geq 0 \\ 0 ~~&\text{for}& x&...
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1answer
47 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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5answers
194 views

Where does $\hat{P}\psi(x) = -i\hbar \partial_x \psi(x)$ come from?

It's a very basic question, where does the relation $$\hat{P}\psi(x) = -i\hbar \partial_x \psi(x)$$ for any square integrable $\psi(x)$ come into existence? Some texts I found states that the above ...
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1answer
49 views

Double Integrals of Force

I took AP Physics C and Multivariable Calculus last year, and noticed something interesting. For non-relativistic particles in one dimension:$$F=\frac{\partial p}{\partial t}=\frac{\partial E}{\...
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1answer
83 views

Eigenstates of position and momentum operators in QM

In Griffiths pages 103-105 "Introduction to Quantum Mechanics" 2nd editiion he states that the eigenfunctions of the position and momentum operators are $$g_y(x) = \delta(x-y)$$ where the eigenvalue ...
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4answers
877 views

The Momentum Operator in QM

I've seen the 'derivation' as to why momentum is an operator, but I still don't buy it. Momentum has always been just a product $m{\bf v}$. Why should it now be an operator. Why can't we just multiply ...
3
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1answer
70 views

Vacuum expectation value in presence of a source

If a vacuum is translationally invariant i.e., $P^\mu|0\rangle=0$ or $e^{(\pm ip\cdot x)}|0\rangle=0$, we can express the the vacuum expectation value of a field as $\langle 0|\phi(x)|0\rangle$ as $$\...
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2answers
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What is $p_T$? (transverse momentum?)

I've been looking at a few papers in experimental physics (from the ATLAS collaboration, for example) and I've often run across phrases such as "high-$p_T$ electron." What exactly is $p_T$? Is it ...
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0answers
12 views

Transverse momentum [duplicate]

I'm having an introduction on detector systems in particle physics. The sources I read constantly talk about the measurement of "transverse momentum". However, I cannot find a definition of what is ...
7
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2answers
147 views

Did Newton conduct any experiments to find something called momentum, or was he such a great genius that he was able to spot it intuitively?

I wanted to go to the depth of the discovery of classical mechanics, instead of just reading, accepting and learning things. Now my question is not a single question, but it can answer many of my ...
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3answers
1k views

What are the general solutions to a hard sphere collision? [duplicate]

Surely someone has found the solutions to the hard sphere collisions (in $n$ dimensions) of two bodies of mass $m_1$ and $m_2$, respectively--that is the resultant velocities (or momenta) of the two ...
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1answer
37 views

Inner product of standard-momentum one-particle states in Weinberg

My question has essentially already been addressed in Questions concerning some parts of the section on one-particle states in Weinberg's first volume on QFT (third question), but unfortunately ...
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1answer
146 views

How to find initial direction of an object using components [closed]

I have a basic (not for me) physics question that I am struggling to get my head around. It involves a car moving at an unknown speed that explodes into 3 pieces. I am having trouble finding the ...
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1answer
58 views

With the descent of Newtonian mechanics is Newton's third law still valid?

Or more specifically, with the standard model, quantum theory and other advances in physics, all those experiments in CERN and other accelerators, was there any occurrence where this law was violated? ...
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3answers
97 views

Moving objects using light

Photon do not have mass but they have momentum, can we use laser to pick up golf ball and hurl it several yards away without burning it into crisp?
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1answer
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Intuitive picture for Mandelstam $t$

In tree-level electron-positron scattering one has two possible channels corresponding to Mandelstam variables $s$ and $t$. The $s$-channel ist fine, there $\sqrt s$ is just the center of mass energy ...
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1answer
26 views

How high does a slide need to be if the person at the bottom grabs a pole and rotates the pole 72 degrees?

My attempt: $mgh = \frac{1}{2}I \omega^2$ $\omega^2 = 2 \alpha\Delta \theta$, so $mgh = \frac{1}{2}I 2 \alpha \Delta \theta$ $mgh = I \alpha \Delta \theta = \tau \Delta\theta$ $\tau = rF\sin \...
3
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2answers
76 views

Throwing masses to gain velocity. A question of efficiency

I was thinking the other day of a system in which you eject mass. And then I wonder whether it was more efficient to throw a big mass or many little. Let me put it in other terms. Suppose you are ...
0
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1answer
61 views

Momentum equation in a Lagrangian configuration

When writing the momentum equation in a lagrangian configuration is the the stress tensor used the first Piola-Kirchhoff stress tensor or the nominal stress tensor (which is the transpose of the 1st P-...
0
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1answer
48 views

Norm of the momentum 4-vector

The norm of the momentum 4-vector is $\mathbf{P}.\mathbf{P}$ $= (\gamma mc, \gamma mv).(\gamma mc, \gamma mv) = \gamma mc^2 - \gamma mv^2$ But why is $\gamma mc^2 - \gamma mv^2 = mc^2$?
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29 views

Quotient Rule in Vector Calculus

Wikipedia gives the quotient rule for (1) the gradient of two scalar fields "$f$" and "$g$" and (2) the divergence of a vector/tensor field and a scalar field "$\boldsymbol{A}$" and "$g$" as $$\nabla ...
0
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2answers
175 views

what is actually mean by momentum in deepest level of physics?

What does something called "Momentum" actually measure?I know that generally momentum of a object is describe by the multiplication of mass and object's velocity and it is a conserve quantity without ...
2
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2answers
188 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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0answers
24 views

Can deformations of time-space continuum violates law of momentum conservation?

Based on Einstein’s theory of relativity a mass as property of physical objects creates deformation of time-space continuum. Therefore the light path bends in gravitational fields of massive objects. ...
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1answer
44 views

Does momentum scale linearly with time, assuming a constant nonzero net force, even at relativistic speeds?

I would expect it to, since you'd think the loss of velocity due to relativity would be made up for by the gain in relativistic mass. I'd like this to be confirmed, though. and if so, in whose ...
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1answer
65 views

How do you determine which way two objects will travel after collision when given their respective masses and speeds?

I was practicing some Mechanics, and I came across a problem that involved an impact between two objects: I understand how to approach the question: Apply the conservation of momentum, and use the ...
7
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2answers
714 views

Conservation of momentum when one body is fixed

When we fire a gun, it recoils. Both bullet and gun gain in momentum. Before the shot, momentum of both is zero. If we make the gun unmovable somehow, after the shot, what will be the effect on the ...
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3answers
111 views

When a bomb explodes, does it momentum remain same?

If, from an aircraft, a bomb is thrown to an object placed at ground and bomb explodes before it hits the object, i.e if it explodes in the middle of its path, does it momentum remain same? I knew ...
0
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4answers
135 views

Why don't two objects move with the same velocity after collision?

I have a problem with understanding the nature of collisions and their outcomes. From my understanding, I come to think that when a mass collides with another, both of them should always have equal ...
3
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2answers
53 views

Momentum conserving delta-function in the transfer matrix of quantum-field-theoretic scattering theory

The $S$-matrix vanishes unless the initial and final states have the same total $4$-momentum, so it is helpful to factor an overall momentum-conserving $\delta$-function: $$\mathcal{T}=(2\pi)^{4}\...