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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Deduction of relativistic mass formula in 1+1 dimensions

I have read the explanation/calculation of relativistic momentum and relativistic mass in the Feynman lectures, see chapter 16.4 here: http://www.feynmanlectures.caltech.edu/I_16.html. (I guess this ...
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125 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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1answer
170 views

Deriving $p = mv$ from translational symmetry (momentum conservation law)?

"In classical mechanics, momentum is defined as the quantity which is conserved under global spatial translations or, alternatively, as the generator of spatial translations." (G.Parisi, ...
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84 views

Lagrangian with vanishing conjugate momentum, independent variables

Given a Lagrangian density $\mathcal L(\phi_r,\partial_\mu\phi_r,\phi_n,\partial_\mu\phi_n)$, for which we find out that for some $\phi_n$ its conjugate momentum vanishes: ...
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3answers
206 views

Effect of incoming force on linear vs. angular velocity

First of all, I should note that I'm a programmer and have only an extremely basic understanding of physics; I only know how to explain my question in layman's terms and I apologize if I'm unclear or ...
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1answer
145 views

Lorentz covariance of the Noether charge

The invariance under translation leads to the conserved energy-momentum tensor $\Theta_{\mu\nu}$ satisfying $\partial^\mu\Theta_{\mu\nu}=0$, from which we get the conserved quantity$$P^\nu=\int ...
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How to get the position operator in the momentum representation from knowing the momentum operator in the position representation?

I know that $$\tag{1}\hat{p}~=~-i\hbar \frac{\partial}{\partial x}~.$$ How can I get $$\tag{2}\hat{x}~=~i\hbar \frac{\partial}{\partial p}~?$$ I think this simple and I'm just over thinking it, ...
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1answer
98 views

Confused about elasticity and collisions

I was solving the following problem and the explanation to it confused me. There are two objects with mass $m$ and $M$, respectively. The object with mass $m$ has a velocity of $\sqrt{2gl}$ and ...
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2answers
164 views

Not so simple problem using momentum, energy and angular velocity…?

I have an object in free space (no gravity) with angular momentum $ = \omega_i $, and some velocity vector $=\vec{V_i}$. To simplify we will say it has a mass-less rigid rod length $ = \ell $, ...
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1answer
53 views

momentum conservation related to varying mass . please help? [closed]

a heap of chain is lying on a horizontal table a small part of the chain is released through the hole in the table . Calculate the velocity of the chain as a function of length of the vertically ...
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1answer
341 views

How to derive or justify the expressions of momentum operator and energy operator?

It has been noted here$\! { \, }^{\text(1, 2)}$, for instance, that $$\mathbf{F} = \frac{d}{dt}\!\!\biggl[ \, \mathbf{p} \, \biggr]$$ is true in all contexts. Likewise, in notable contexts it is ...
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1answer
294 views

Harmonic Oscillator Energy to Momentum Expectation Value

If we are given a wave function written in terms of harmonic oscillator energy eigenfunctions how can we determine the maximum possible momentum expectation value? It's a combination of the first two ...
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1answer
635 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 ...
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3answers
250 views

conservation of momentum when a bullet hits a block

why momentum is conserved when a bullet hit a block horizontally even when force of bullet is acting on it and net external force is not zero ?
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2answers
107 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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3answers
454 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 ...
2
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3answers
2k views

Why does rubber ball bounce back while iron ball doesn't?

Suppose there are two balls, one of rubber and the other metallic. There are of the same mass and are thrown on a wall with the same velocity. Why does a rubber ball bounce back while a metallic ball ...
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1answer
112 views

Changing Momentum

Okay, so I am having a hard time wrapping my head around this. Before looking at the answer, I worked the example and got the answer only because I used dimensional analysis to get me to the right ...
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2answers
6k views

Perfect elastic collision and velocity transfer

So my teacher told me that when you have two identical balls in a perfectly elastic collision, the first ball A will collide with B and afterwards A will stop and B continue. Why is this? Doesn't ...
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2answers
87 views

Identity in quantum operator tutorial

I'm reading this tutorial by Ben Simons entitled Operator methods in quantum mechanics in connection with his course in advanced QM, and I'm a bit puzzled by an identity in page 25, a bit above ...
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1answer
200 views

Muon 3 Body Decay

I'm trying to calculate the maximum energy of the electron in the decay muon >electron + electronantineutrino +muonneutrino in the reference frame of the muon having no kinetic energy. $m_m$=mass of ...
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30 views

Electromagnetic Energy and Momentum

I'm trying to show that the electromagnetic energy density and momentum density satisfy the inequality: $ u \geq c |\vec{\wp}| $, where $\wp$ is the momentum density and $u$ is the energy density. I ...
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2answers
3k views

How to find the compression of a spring attached to an object [closed]

I am having some trouble figuring out the equation needed to solve this problem. A 3.0-kg block slides along a frictionless tabletop at 8.0 m/s toward a second block (at rest) of mass 4.5 kg. A ...
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4answers
253 views

A question abou $E=pc$ for massless particles

Since photon has no (rest)mass and $$E^2=(pc)^2+(mc^2)^2$$ we derive that $E=pc$ for particle with no (rest)mass. However, if we transform the non-relativistic formula for kinetic energy ...
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2answers
775 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
508 views

Punching - Force or Momentum?

If I want to punch a person inflicting maximum damage, what do I need to care about? My force of punching, i.e, do I need more acceleration? Or do I need momentum, i.e my velocity for punching?
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48 views

Is there a heuristic argument for the expression $ \textbf{g} = \frac {\mathbf{S}}{c^2}$?

Electromagnetic momentum density and the Poynting vector are related by the simple expression: $$ \textbf{g} = \frac {\mathbf{S}}{c^2}$$ It can be rigorously derived from Maxwell's equations, but is ...
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84 views

Rocket hovers- and then what?

If we have a rocket, using conservation of momentum we derived in my classical mechanics course $$m\dot{v}=-\dot{m}v_{ex}+F^{EXT}$$ $m$ is the total mass of the rocket and fuel still on the rocket ...
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2answers
620 views

Why does the amount of energy transferred depend on distance rather than time?

The change in energy of an object can be determined by the work equation, where work is the change in energy: $$ W = F \cdot d $$ I conceptualize the transfer of energy as simply a series of small ...
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357 views

projectile that splits into two fragments of equal mass

I am studying for an exam, and this is part of a problem in my book. A projectile is launch from level ground and is intended to hit a target 100m away. Instead, it explodes into two fragments of ...
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195 views

Angular Momentum Conservation in Gravitational Interaction

thanks for any help. I'm trying to show that in a 2body problem, angular momentum is conserved given that $\dfrac{dp}{dt}=\dfrac{-GMm(rv)}{r³}$, where p is momentum, t time, G gravitational constant, ...
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1answer
94 views

How does a “hammer thrower” that we see in the Olympics, impart so much momentum

How does a "hammer thrower" that we see in the Olympics, build so much momentum into the club? It's sort of like the golf swing, the more momentum, primarily in the club head, the further the ball ...
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31 views

Trouble evaluating an integral arising from particle collision

Assume we have two charged particles colliding. He have particle 1 with mass $m_1$, charge $Z_1 \cdot e$ which travels in $x$-Direction passing by a STATIONARY particle 2 (mass $m_2$, charge $Z_2 ...
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3k views

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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2answers
192 views

Why does a stationary force affect the conservation of momentum, but not the conservation of energy?

Let's say I have two positive charges approaching one another at the same speed with only their mutual forces acting on one another. Total momentum (= 0) and energy is conserved and the charges ...
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1answer
833 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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743 views

Are principle of Conservation of energy and principle of conservation of momentum consequences of Newton's laws?

It is known that principle of Conservation of momentum and principle of conservation of energy are two fundamental principles of physics.But in RP Feynman's Lectures of physics, in the chapter of ...
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1k 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
96 views

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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3answers
443 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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2answers
383 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
102 views

How is momentum conserved when a magnet attracts a metal?

Suppose your have any magnetic object and no external force acts upon it, and the object comes near a metal which causes an impulse (think that will happen). However, the magnetic force is internal to ...
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1answer
99 views

Storing kinetic energy in bonds

Let's assume a setup with a static linear molecule with three identical atoms connected by bonds and a single atom, identical to the other three, being shot at the molecule. Let's also assume that ...
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3answers
445 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 ...
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2answers
163 views

How to work out momentum when there are velocity and mass changes

I have a pretty simple homework question, but I can't rap my head around it. In the question a swimmer of $55 \mbox{ } \mathrm{kg}$, jumps off a stationary raft of $210\mbox{ }\mathrm{kg} $. The ...
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1answer
92 views

Question about Cars: Momentum

Car B rests at the bottom of a frictionless inclined plane. In order to travel a height of 0.6m and maintain a speed of 2 m/s at the end of the track it needs to start with 4 m/s. a) If ...
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4answers
2k 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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259 views

Which parameter determines how much the 'recoil' or force applied by an object hurts?

Another question from my textbook, directly following after this question: 2 identical bullets are fired, on from a lighter rifle and one from a heavier one, with the same amount of force. Which ...
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1answer
175 views

Theoretical considerations on the conservation of energy and the conservation of linear momentum

I report to you an interesting excerpt from my Physics book. It is an Italian version, so I apologize in advance, as I'm sure I won't give proper justice to its beauty in the translation as the ...
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1answer
175 views

Calculate force of impact on running dog

I'm going to hold a dog protection tournament. I'd like to give the audience information about the force of the impact of the running dog when it hit(attacks) the decoy on a huge screen. I'm a ...