Questions tagged [momentum]

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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Beam momentum positive/negative sign

Could anyone explain to me why the momentum of this isostatic beam in $A$ is negative instead of positive? Why isn't it as simple as $+FL-FL/2 = +FL/2$?
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A Second Geodesic Equation?

I have a question about the geodesic equations. I understand the following formulation of it: $$\frac{d p^\mu}{d\tau} = - \Gamma^j_{v\mu}p^vp^\mu.$$ However, I was reading https://arxiv.org/abs/1305....
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Proof that momentum operator acting on a wavefunction gives the expectation value

I'm following a book where the author tries to prove that $$\langle p \rangle = \langle \psi \vert \hat{p} \vert \psi \rangle,\tag{0}$$ so he just computes the integral $$ \langle \psi \vert \hat{p} \...
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Why are certain quantities so fundamental to physics? [on hold]

Apart from having a qualitative description of quantities such as momentum, work and energy, why are these quantities considered so fundamental? What is the reason to define them in the first place? ...
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Kinematics of a Rigid Body; Thin plate rotated about a point [on hold]

I need help with this setting up this equation. So far I have after taking the moment about $O$: $$100(1-e^{-0.4t})-0.75mg\sin{\theta}= \left[\left(\frac{1}{12}m(l^{2}+l^{2})\right)+md^{2}\right]\...
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Will momentum be conserved in case of electrostatic force?

If a charged particle approached another particle of same charge held by some external force, then by coulomb's law the particle will start electrostatic repulsion. Thus coming to a closest distance ...
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What's the momentum-space vacuum wave-functional of a fermion?

In the Schrödinger picture, the field eigenstates of a real scalar field $\hat\phi(\mathbf x)$ with $\mathbf x \in\mathbb R^3$ are the states $\hat\phi(\mathbf x)|\Phi\rangle=\Phi(\mathbf x)|\Phi\...
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Is Kinetic energy always conserved in an elastic collision/impact?

While working out through some problems I encountered this problem : A ball moving with a velocity $v$ hits a massive wall moving towards the ball with a velocity $u$. An elastic impact lasts for ...
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What's wrong in my approach towards solving this problem?

This is the problem that I have to solve: The figure shows a block $A$ of mass $6m$ having a smooth semicircular grove of radius $a$ placed on a smooth horizontal surface. A block $B$ of mass $m$ ...
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Why can I use conservation of momentum to understand a bag getting dropped on a moving truck, if the ground provides an external force?

Please help me with this sat question from released test A toy truck with a mass of $0.6$ kg initially coasts horizontally at a speed of $2$ meters per second. A child drops a beanbag with a mass ...
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Find coefficient of friction [closed]

A plank P and a block Q are arranged by keeping block Q on the extreme left of plank P. The surface between P and Q has friction whereas coefficient of friction between plank P and ground is zero. ...
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Actuator disk: how to find the shape of stream-tube? [closed]

I am trying to understand how one can derive the shape of the stream tube created by an actuator disk shown here To be more precise,can anyone please point out how can I find the area of the stream ...
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1answer
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Physical significance of the canonical energy-momentum tensor

I have a question regarding the physical significance of the canonical energy momentum tensor $T_\nu ^\mu$ in the context of classical field theory. It is defined as $T_\nu ^\mu = \frac{\partial \...
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4answers
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A man with a rifle shoots bullets at a speed [closed]

Hello all So I was doing this question. I had a doubt that, initially as both the (man and rifle ) system and the bullet were at rest we put 0 instead of m1u1 + m2u2 in equation of conservation of ...
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Lorentz boost in light-cone coordinates

Consider a particle with momentum $p^{\mu}=(p^+,p^-,p_{\perp})$, where the momentum is written in light cone coordinates defined as, \begin{align} n^{\mu}&=(1,0,0,1)& \bar{n}^{\mu}=(1,0,0,-1) ...
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Is “physical damage” proportional to momentum or kinetic energy? [duplicate]

If a rock is thrown at someone's head, or a car drives against a wall, or a meteor hits a planet, is the physical damage done to the object proportional to the projectile's momentum, or to its kinetic ...
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Canonical or mechanical 4-momentum to measure energy?

I've often seen that the energy of a particle $p$ with 4-momentum $p^\mu$ measured by an observer $O$ with 4-velocity $u^\mu = dx^\mu/d\tau |_O$ is given by $$E=-p_\mu u^\mu.$$ In general, what ...
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Why does a particle, e.g. a proton, at rest have $v=0$?

Given the formula $E=mc^2$, the mass is equivalent to energy through the speed of light. This equation is also the special case of $E^2=(mc^2)^2+(pc)^2$ when $p=0$. Thus, it is at rest respectively ...
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Does the law of conservation of momentum mean both linear and angular momentum?

I was solving a problem where a bullet hit a rod hinged about one of its ends. The rod is standing vertically before the collision. We had to find the final angular velocity of the rod. The way we did ...
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Helicity of massless particle in Weinberg book

In Weinberg The Quantum Theory of Fields Vol.1 in eq (2.5.39) page 72 he has $$J_3 \Psi_{k,\sigma}=\sigma\Psi_{k,\sigma}$$ Where $J_3$ is the rotation generator in the $z$ direction. Than he calls $...
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Underdetermined Problem with “Spring Launchers”?

Consider the following preliminary problem. A box of mass $m$ is attached to a box of mass $M$ by a compressed spring, and both are moving at velocity $v_{0}$. The compressed spring has potential ...
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Differing results from different conservation laws

I am currently studying for the GRE Physics subject test by working through published past tests. My question is about problem 44 from the test GR8677: $44.$ A uniform stick of length $L$ and ...
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Does increasing energy mean there is an external force?

So, in one of the online lectures that I was watching, Walter Lewin did an experiment to prove the law of conservation of momentum. There were two cars, attached to each other by a spring (The cars ...
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Conservation of momentum — arm hitting object

Suppose I strike an object with my hand and I stop moving my hand as soon as I make contact with the object. This sends the object moving in a straight line with some velocity. Part 1: Is it valid to ...
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Calculating the exhaust velocity using conservation of momentum [closed]

I was just wondering if i did this correctly $$p_{exhaust}=-p_{rocket}$$ $$m_{e}v_{e}=-m_{r}v_{r}$$ $$v_{e}=\frac{-m_{r}v_{r}}{m_{e}}$$ I used data from a Saturn V simulation by Robert A. Braeunig ...
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Why isn't the water moving when it is undergoing electrolysis

I understand that in electrolysis of water, the water around cathod is splited in the way of 4H2O + 4e => 2 Hydrogen + 4 OH- . And the hydroxide will move to the anode due to electric field in the ...
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3answers
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Expected value of Momentum in a square infinite well [closed]

Say I have a particle with mass $m$, in a potential infinite well centered at $x=0$ with length $d$ which wave function at $t= 0$ is represented by: $$\Psi(x)=\begin{cases} \frac{1}{\sqrt{2}}\left[\...
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Possible mistake in the solutions? [closed]

This is from Kleppner's introduction to mechanics and I've been having trouble making sense of the solution in the solution manual for quite a while and I've concluded that its wrong but I need some ...
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How does light transfer momentum to a solar sail?

Last month the Planetary Society launched Solar Sail 2. After reading about it a bit I found that its a type of payload carrier that works on the principle of transfer of momentum from light. ...
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Why do the surfaces in contact of two colliding balls deform?

I've been told that it happens because the surfaces in contact must travel equal distances in any time interval as long as they are in contact. Could someone explain this in a different manner?
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Why are 2 gamma photons created? [duplicate]

When a positron and an electron come together they annihilate and produce 2 gamma photons $$e^+ +e^- \rightarrow 2\gamma$$ I can understand that they must be produced in pairs to conserve momentum. ...
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How can momentum be 0 in a center of mass frame?

I was watching one of Walter Lewin's lectures, in which he mentions that the total momentum of a system in the center of mass frame is always 0. I don't quite understand this. Here is an example which ...
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1answer
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Spectrum of the momentum operator for free Dirac fermions on a lattice

I am studying lattice field theory and would like to understand the momentum operator for free Dirac fermions on a square lattice. In this case one needs to discretize the momentum operator (which ...
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Momentum operator in QM - scalar or vector?

The momentum operator for one spatial dimension is $-i \hbar d/dx$ (which isn't a vector operator) but for 3 spatial dimensions is $-i\hbar\nabla$ which is a vector operator. So is it a vector or a ...
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What do these momenta mean? [duplicate]

I'm studying the motion of photons near a Schwarzschild black hole. My coordinates to describe the position of a photon are $~r$, $~\theta$, $~\phi$ and $~\textrm{p}_\textrm{r}$, $~\textrm{p}_\...
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How does a heated object lose thermal energy in a perfect vacuum?

Suppose I heat up an arbitrary object to an arbitrary temp and then place it in a near perfect vacuum (let’s assume inter-galactic space). If there is essentially nothing for the object to transfer ...
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What does the expectation value of canonical momentum physically mean?

In Quantum Mechanics, there seem to exist two types of momenta, namely kinematic momentum and canonical momentum, both of which are $$ p(t) = \mathscr{U}^\dagger i\hbar \frac{\partial}{\partial x}\...
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Why Didn't the Energy-Momentum Relation Work?

I am currently studying for the GRE Physics subject test by working through published past tests. My question is about problem 20 from the test GR8677: A positive kaon ($K^{{}+{}}$) has a rest ...
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0answers
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Four-momentum of a photon emitted from an accretion disk

Consider a non-rotating compact object surrounded by a revolving accretion disk. A distant observer sees the disk in an edge-on position. The center of the disk may be taken as the origin of $r-\theta-...
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Wavelength of a particle [duplicate]

As we know wavelength of a particle is equal to (Planck's constant / momentum), so here momentum $= mv$ where $m$ is a mass of an object and $v$ is the velocity of an object. What will happen when ...
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In special relativity is mass just a measure of all other energy than kinetic?

The energy momentum equation in special relativity is: $$E^2=(pc)^2+(mc^2)^2.$$ and it holds for a moving but not accelerating object. One special case is the massless photon: $$E=pc.$$ And another ...
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Varying of momentum for constant kinetic energy

How is that If the momentum of the particle is constant with time, its kinetic energy ($E_k$) should also be constant with time a true statement but the converse is false... When momentum is ...
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3answers
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Energy Loss in Inelastic Collision

If we take a tennis ball and drop it from a certain height above the ground on earth, it collides inelastically, with the maximum height it can reach reducing after each collision due to loss of ...
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1answer
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Momentum Wave Function gives strange expectation values

Suppose there's a particle with the wave function $\psi(x)=\frac{1}{\sqrt{L}}$ for $0<x <L$ and 0 everywhere else. One way to get the associated Momentum Wave function is direct integration on ...
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Forces/momentum/impulse repartition and balancing over several rigid bodies touching each other

I've got a problem about physics modeling in a really particular case. I'm not exactly sure if i have to ask it into physics or gamedev,but i suppose the problem is best suited here, since it is about ...
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Newton's third law in magnetic in magnetic fields

Say I have a charged particle moving through a magnetic field perpendicular to it. It will experience a force, but according to Newton third law Every force has an equal and opposite reaction. So ...
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Is Impulse Frame Independent?

The title says it all. I was wondering if the impulse on an object would change if we look from another inertial or non-inertial frame of reference. According to me it shouldn't, since the force ...
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Does throwing a penny at a train stop the train?

If I stand in front of a train and throw a penny at it, the penny will bounce back at me. For the penny to reverse its direction, at some point its velocity must go to zero. This is the point it hits ...
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1answer
118 views

Trying proving that energy and momentum are conserved in every inertial frame

I'm trying to show, using Lorentz transformations, that if relativistic energy and momentum are conserved in $S$, then they are conserved in $S'$ too. A wrong proof Let's suppose I know that in ...
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1answer
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Linear momentum of a rotating system

So say we have a thin rod resting horizontally on a flat frictionless surface. The rod is pinned at its center, and a small mass collides perfectly inelastically with one end of the rod after moving ...