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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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
64 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 ...
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2answers
377 views

Ball flying towards me - Newton's third law is violated?

I was trying to answer the question of the flying ball here on the basis of Newton's third law and momentum conservation. Here is what I have tried. Lets take a ball mass of $m_1$ (index 1 is the ...
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2answers
132 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 ...
6
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1answer
445 views

Derivation of force law in special relativity

I've seen force defined in special relativity as the rate of change of 4-momentum $$ {\bf{F}} = \frac{d {\bf{p}}}{dt} $$ Can anyone comment on the following derivation of that relation? Take one ...
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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 ...
0
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1answer
35 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
144 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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1answer
45 views

Momentum Conservation

The Problem: There are three masses all of equal mass $m$. One mass breaks of with velocity $v$ at an angle $\theta$ to the rod. I have to find max velocity of $A$ and the time at which this ...
2
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3answers
96 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?
1
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1answer
41 views

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 ...
0
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1answer
25 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
75 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
47 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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0answers
27 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 ...
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2answers
168 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
185 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 ...
0
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0answers
23 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 ...
0
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1answer
58 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
710 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
98 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 ...
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4answers
121 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
46 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}\...
3
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1answer
47 views

Are asymptotic states in scattering experiments really momentum eigenstates?

In a typical collider experiment, two particles, generally in approximate momentum eigenstates at $t=-\infty$, are collided with each other and we measure the probability of finding particular ...
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6answers
10k views

What is canonical momentum?

What does the canonical momentum $\textbf{p}=m\textbf{v}+e\textbf{A}$ mean? Is it just momentum accounting for electromagnetic effects?
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0answers
15 views

How could you slow down or change direction with photonic propulsion?

So you have a laser shooting at a sort of solar sail to transfer momentum in the forward direction but could you have an onboard laser and turn the laser around to hit another sail? How could you turn ...
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0answers
20 views

Invariant amplitude in QED in terms of Mandelstam variables [closed]

So I'm having a little trouble with this question: These are my workings thus far: I just can't seem to get certain terms to vanish. I have the 1/4 factor for going between $8e^4$ to $2e^4$. Is ...
0
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1answer
39 views

Momentum equation of a beam hitting a stationary target to create antiprotons

I'm struggling with the solution of a physics exercise which is to calculate the minimum energy needed to create antiprotons when a proton beam scatters on a stationary proton target: $$p + p \...
0
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1answer
33 views

How to calculate impulse required to move an object vertically upward by given distance [closed]

Suppose I have a stationary object of mass $m$ and I want to apply a momentary force in the vertical direction so that it just reaches the height $h$. So how do I calculate the impulse required in ...
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0answers
69 views

Zeroth component of 4-momentum and relativistic energy-momentum relation

As I understand it one is forced to use 4-vectors since we require objects that transform as vectors under application of Lorentz transformations and 3-vectors do not (technically they do under ...
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1answer
35 views

Variation of Veritasium bullet block experiment

I'm new here. this is in reference to the video posted by veritasium on the bullet block experiment. i realise there is already a thread on this but i want to ask a variation of the question. so ...
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2answers
268 views

Why do particles of equal mass (with one at rest) undergoing elastic collisions scatter at only right angles?

This is from the Section 9.6, page 351 of "Classical Dynamics of Particles and Systems" by Thornton and Marion. By setting a up a system where mass 1 has initial momentum $m_1 u_1$ and mass 2 is at ...
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0answers
14 views

Momentum conservation problem, elastic collision [duplicate]

This question has got me thinking for a while now and I haven't been able to come up with any answer at all. I've done the basic conservation of momentum, kinetic energy but I have no idea how to ...
0
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2answers
43 views

Momentum of a rack and pinion gear system excited by a time variant force

Background I have a rack and pinion gear system as shown in the image below The pinion gear is attached to a flywheel at the back. The first state of the system, none of the gears or the ...
21
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5answers
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How can there be net linear momentum in a static electromagnetic field (not propagating)?

I understand from basic conservation of energy and momentum considerations, it is clear in classical electrodynamics that the fields should be able to have energy and momentum. This leads to the usual ...
0
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0answers
32 views

Relating Initial velocity and acceleration to distance traveled up a ramp

This is the situation: I am conducting research on the ability of fin-fish to scale short wetted ramps for use alongside sea-lamprey barriers to allow non-target species to pass these barriers. We ...
0
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1answer
30 views

Why is the acceleration of the center of mass is equal to 0 in this problem?

I don't understand why the center of mass' acceleration is equal to 0 when the center of mass should be moving as an external force is exerted on the cue ? Billiard Balls. Now we can go back and ...
3
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3answers
162 views

Center of mass motion and variation of mass

Here are the proofs regarding the center of mass motion as reported on my book. $$\vec{r_{cm}}=\frac{\sum\vec{r_i} m_i}{\sum m_i}$$ $$\vec{v_{cm}}=\frac{d{\vec{r_{cm}}}}{dt}=\frac{1}{M}\sum \frac{d}{...
4
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2answers
106 views

Is the eigenvalue of Hamiltonian invariant under linear transformation of momentum operator?

It is given The dynamics of a particle moving one-dimensionally in a potential V(x) is governed by the Hamiltonian $H_0 = p^2 /2m + V(x) $, where $p = -i\hbar d/dx$ is the momentum operator. ...
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1answer
36 views

Question about Thrust; am I correct?

Basically, here's what I understand about Thrust: Thrust is a force. You get it by doing $v\times\frac{dM}{dT}$. Pretty basic, because that's the formula you're given. However, because I'm trying to ...
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1answer
23 views

What is the minimal G-force curve in 2-dimensional space?

Given two parallel roads, which need to be connected, what shape of curve would produce the minimum overall horizontal G-force(s) on travelers? Is it a $sin$ or $cos$ wave? Is it a basic cubic ...
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1answer
49 views

The ratio of masses in an elastic collision [closed]

Two blocks of mass $M_1$ and $M_2$ moving along a 1-dimensional straight line with velocities $V_1$ and $V_2$, respectively, collide elastically. After the collision they move with respective ...
0
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1answer
26 views

When to consider friction as an impulsive force?

Suppose a ball obliquely strikes a rough horizontal surface then it experiences a frictional impulse and conservation of linear momentum cannot be done on the horizontal direction. Now consider ...
1
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1answer
28 views

Is it possible to measure the spin of an electron without moving it?

I know that the position and spin operators commute, so it is theoretically possible. What I want to know is, what experiments currently exist that achieve this?
0
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1answer
19 views

Spheres collide with merry-go-round [closed]

Four spheres, with uniform densities $\rho_1, \rho_2, \rho_3, \rho_4$ and radii $r_1, r_2, r_3, r_4$, respectively, roll without slipping with constant velocities $v_1, v_2, v_3, v_4$ along tracks ...