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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Why isn't jumping against a wall an elastic collision?

According to this calculator http://www.abecedarical.com/javascript/script_collision1d.html when low mass object hits high mass object it is reflected gaining opposite velocity almost the same as ...
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192 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
51 views

Obtaining momentum operator $P^\mu$ from Lagrangian and energy-momentum tensor $T^{\mu\nu}$

I am pretty new to quantum field theory. Given the Lagrangian density, $$ \mathcal{L} = \frac{1}{2} ( \partial_\mu \phi ) ( \partial^\mu \phi ) - \frac{1}{2} m^2 \phi^2 $$ and its energy-momentum ...
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83 views

In a CMCS 2-body system, why does the speed of the particles after collision stay the same?

A particle $m_1$ is traveling with velocity $v$ toward a stationary particle $m_2$. The velocity of the center of mass is given as $v_c=\frac{m_1}{m_1+m_2}v$. Changing to a moving coordinate system, ...
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67 views

calculating electrodynamic momentum of a dumbbell (consisting of two point charges) in longitudinal motion

I'm working through a paper on momentum in electrodynamics that requires the integration below and would greatly appreciate any help. I'm pretty sure it evaluates to $2/d$ but I can't quite figure ...
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1answer
27 views

Equations for a collision between two particles

Say I have two particles on a 2D plane, they have a x and y coordinate, a x and y velocity, a mass, a coefficient of restitution and a coefficient of friction. What formulae would I need to determine ...
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1answer
31 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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32 views

Pressure, Momentum and Energy: A 'Peculiar' Relation

Is the following possible? $$ P = \frac{p^2}{3E} $$ where $P$ is pressure, $p$ is momentum and $E$ is energy. In what convention is the above relation acceptable? EDIT: The source paper can be found ...
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41 views

Transformation of $q_k$ and $p_k$ from invariance of Hamiltonian

This is a step in Nakahara's Geometry, Topology and Physics, 2nd edition, 2003, on pages 7-8: Given that $q_k ' = q_k +\epsilon f_k(q)$, we have that $$\Lambda_{ij} = \frac{\partial q_i'}{\partial ...
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1answer
46 views

Why we can omit some forces while applying linear momentum principle

While applying linear momentum principle, namely that if force is zero linear momentum of the system is constant, in textbook they don't count for $N$ force from $M \to m.$ This force have component ...
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1answer
26 views

Conservation of generalized energies in Newtonian and Relativistic Systems

I was considering the following problem: In a closed system, it is assumed that mass, momentum and energy is conserved. If we label the total mass of the System $M(i)$ at a time i, the total Momentum ...
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107 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 Newtons third law and Momentum conservation. Here is what I have tried. Lets take $m_1$ (the ball) hits $m_2$ (the man). ...
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1answer
93 views

Changing momentum of moving trolley

We have a trolley of mass $m$ and it is moving at a velocity $v$ along a smooth horizontal plane. It is full of water, and is leaking water at a constant rate out of the bottom of the trolley, i.e ...
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54 views

The question about MTW 4-momentum integral expression and lorentz nature

In section 5.8 of Misner, Thorne, and Wheeler's "Gravitation" there is a proof that 4-momentum determined as $$ \tag 1 p^{\mu} = \int T^{\mu 0}\,\mathrm{d}^{3}\mathbf r , \quad \partial^{\mu}T_{\mu ...
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475 views

Practice AP Physics B Exam Question regarding Momentum

I am trying to review momentum for the AP exam coming up. I will be taking the AP Physics C exam for Mechanics, but I was just practicing on any free response questions I could find and I came across ...
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100 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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159 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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53 views

Is there a general formula to translate from *canonical* to *physical* momentum?

In Peskin and Schroeder, after having derived a conserved tensor $T^{\mu \nu}$ associated with translations in space-time (the stress-energy tensor), it is said that the charges $\int d^3 x T^{0i}$: ...
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34 views

Making An Energy Momentum Plot For A Rashba Model (Using Discretization)

I want to make a plot of the Energy versus the Momentum of the Rashba model, using discrete matrices. First Ill show how I did this for the free particle. Subsequently I will show what goes wrong for ...
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62 views

Momentum of capacitor in a uniform magnetic field

We are observing ideal, charged, parallel plate capacitor placed in uniform magnetic field parallel to plates. Whole system is at rest and isolated (we have forces that hold plates separated, but net ...
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86 views

Hidden momentum

I'm trying to learn about hidden momentum. After reading what I could find with a google search, I understand that it is equal to the momentum carried by radiation, calculated with the Poynting ...
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19 views

In momentum theory, what happens if atmospheric velocity is larger than outflow velocity?

I am currently reading up on aerodynamics, essentially the actuator disk concept and momentum theory as it is described in e.g. Basic Helicopter Aerodynamics by Seddon and Newman. There they assume ...
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63 views

What does the relation between mass and energy of a free particle mean?

What does the Hamiltonian for a free particle mean? Does it mean that the kinetic energy of the particle is in reverse relation with mass? $H$ or $E=\hbar^{2}k^{2}/2m$. Or better to ask: what's the ...
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67 views

Four-momentum, four-velocity, energy

If given the four-momentum of any particle monitored by an observer as: p = $p^\hat{α}e_\hat{α}$ using unit vectors in observer’s reference frame and u = $e_\hat{0}$ then I get I'm just ...
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117 views

The relationship between angular and linear momentum

Why is orbital angular momentum not 0 when spin and linear momentum are not collinear? Why can it be 0 when spin and linear momentum are parallel? Like in the example of a scalar field at rest ...
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74 views

Poynting Vector Volume Integral Inside a Cavity

Given an electromagnetic wave in resonance mode in a vacuum cavity inside a perfect conductor, on the boundary, the parallel component of $E$ field vanishes, and the perpendicular of component of $B$ ...
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108 views

Particle In a Box and momentum, velocity

So on a homework assignment, we are give the width of a well, $a$, and the mass of the particle $m$ and we want to find the average velocity of the particle at the n=1 state. So here is my attempt at ...
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108 views

Including special relativistic effects in momentum in Heisenberg's Uncertainty Principle

I've been told that an electron is somewhere within the space of $10^{-10}m$ and am supposed to find the uncertainty in its velocity. Simply applying $m\Delta x \Delta v \geq \frac{h}{4\pi}$ results ...
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32 views

electron spin separation

I am having doubt whether the electron's up spin moment and down spin moment can be isolated from one another. If it got separated, will each moment acts as magnetic monopole (stable or unstable). ...
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82 views

Force needed to change momentum, from fixed position

I have a situation where I want to change the velocity of a mass, by applying a force from a fixed position. For example in the diagram below, the mass starts with the initial velocity in the upper ...
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568 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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228 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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32 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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59 views

Two impulses on body

Say I have a physics simulation with a single body with three degrees of freedom (two axis and rotation). I have two impulses of equal magnitude in opposite directions. When applying these impulses in ...
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36 views

How do I find the force from drop shock using material properties?

I am dropping a cylindrical cast iron bar with a know elastic modulus and poisson's ratio, $E_{1}$ and $v_{1}$, onto a flat beam of elastic modulus, $E_{2}$ and $v_{2}$ so there is tangential drop ...
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78 views

about wavefunction and vector entries

I am beginer of physics and I am studying some very fundamental idea of quantum mechanics by myself. In the introducing book I am reading, there is an example to show a particle diffraced by a slit or ...
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100 views

Physics behind 2 different wall kicks

I'm looking at a situation where a sprinter starts at some distance x from a wall. The goal is to sprint to the wall, hit it, and get back to the start as quickly as possible. There are two ways ...
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21 views

Scenario of momentum conservation in center of mass - with a ball within a tube

Given the following scenario: The mass of the tube is $m$, and also the mass of the ball is $m$. Radius of the tube is $a$. There is no friction. The system is placed on an horizontal table ($mg$ ...
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36 views

Possible Lack of Invariance in Two Inertial Reference Frame Scenarios

Two objects are connected together via a ideal spring which is compressed initially. Then the spring is released, the two balls are no longer connected and go their separate ways. Assume no other ...
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30 views

How much energy and momentum is carried by a mechanical wave?

Let's assume there is a wave spreading across in a substance. Described by some partial differential equation. How can I calculate the momentum and energy carried by this wave? Or maybe the energy and ...
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49 views

Two cars colliding with different speeds

If I have one car travelling at 30 m/s and another travelling at 10 m/s both weighing the same amount, why is it that the car travelling 10 m/s would have more damage? According to Newton's third law ...
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13 views

Low-momentum behaviour of a short-range potential

I've read the follow sentence in a journal article (arXiv preprint) which constitutes part of my coursework. As discussed in the previous section, the low-momentum behavior of any short-range ...
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15 views

Calculate the distance travelled by hot air before it looses its momentum

Hot air is released from a nozzle with certain velocity into the atmosphere. As the stream travels, it looses momentum and after some time mixes with air.How can we calculate the distance the stream ...
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111 views

Momentum operator in Dirac formalism

Could you derive the momentum operator as follows: Since $\mathcal{T}(\Delta x)=\exp(-ip_{x} \Delta x/ \hslash)$, if we set $\Delta x=x-0$ then it follows that $\left \langle x\right | ...
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26 views

Definition of momentum-entangled particles

When we can say that two particle are momentum entangled ? I just read an article where it's said that two momentum entangled particles share the same momentum value in opposite directions no matter ...
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105 views

Change of QM Momentum operator under coordinate transformation

Can any one please let me know what is the general procedure to construct the momentum operator under some coordinate transformation? For example, I understand that if ...
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154 views

Calculating rotor torque out of mass center

Suppose I have an engine with propeller. I know there is aerodynamic force pushing the propeller opposite direction the engine is turning it. One component of this force is creating lift, but second ...
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74 views

Need help with relativistic dynamics

I understand the concept, but I'm having a hard time applying the consequences of conservation (energy/momentum). For example: A proton with kinetic energy 437 MeV hits a proton at rest elastically ...
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0answers
416 views

Nuclear reaction: creation of deuterium

A proton p collides with a neutron(at rest) n at relatively low-energies and creates a 'deuterium-core' d: $$p+n->d+\gamma$$ Find the wavelength for the photon as a function of the proton's ...
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632 views

Error Analysis, Change in momentum, Kinetic Energy

If momentum of an object is increased by 10%,then its kinetic energy will be increased by? Well, I don't need the solution logically by calculating the change in Kinetic Energy etc, but my question ...