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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Conservation of momentum and conservation of energy

I had the impression that conservation of momentum is valid only when we consider no loss of kinetic energy into heat etc. My tutor says that even if we have loss of kinetic energy as heat in a ...
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3answers
133 views

Momentum operator representation

If $\hat{p}$ acts on position eigenstate, it is $$\tag{1}\hat{p}\left|x\right\rangle=+i\hbar\frac{\partial }{\partial x}\left|x\right\rangle .$$ But in general $$\tag{2}\hat{p} = -i\hbar ...
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1answer
39 views

Path of a swinging object on a rope [on hold]

With my lanyard in hand (weighted by my keys), a gentle swinging motion will put the keys in pendulum motion, swinging back and forth. Pendulum motion is relatively easy to model since it is ...
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45 views
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46 views

What is relationship between linear and angular momentum?

I'm confused about imparting momentum to a sphere, which causes it to rotate without slipping. Does the momentum applied go: only to the rotational motion and the linear is a consequence of the ...
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3answers
192 views

How can I solve this quantum mechanical “paradox”?

Let a (free) particle move in $[0,a]$ with cyclic boundary condition $\psi(0)=\psi(a)$. The solution of the Schrödinger-equation can be put in the form of a plane wave. In this state the standard ...
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1answer
47 views

What makes cart with a moving object in it gain speed (no friction anywhere)?

I would like to understand what makes the cart below the moving object move. There is no friction between any of the objects. The cart is moving therefore there is force applied to it. The only force ...
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5answers
3k views

Why Does Angular Velocity Increase as Radius Decrease?

Suppose a child were to ask you why a tetherball (picture below) seems to speed up as it wraps around the pole. How would you explain this to them? Certainly you wouldn't say something like, "Angular ...
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0answers
26 views

The physics of an anvil [on hold]

I am trying to understand how an anvil might best be made. An anvil requires two essential characteristics: enough hardness to not be deformed under the blows of the hammer, but as little rebound and ...
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1answer
38 views

Calculating post-collision velocity [on hold]

Consider two persons $p1$ and $p2$ of the same mass , such that they are together moving rightward with a velocity of $v/2$ Now person $p1$ pushes $p2$ in the left direction. According to newton's ...
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0answers
35 views

m1v(initial) +m2v (initial) = m1v (final) +m2v(final) [on hold]

Perfectly elastic collisions. Imagine two billiard ball on the table. Ball A has a mass of 2 kilograms and the ball B has a mass of 3 kilograms. the initial velocity of ball A is 9 meters per second ...
2
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2answers
4k views

Inelastic collision and conservation of linear and angular momentum

Is it possible for two spheres (a & b) to have an inelastic collision with BOTH the total linear and angular momentum preserved? I'm doing some physics simulation of some spheres attracting each ...
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2answers
192 views

Changing momentum of moving trolley

Consider a trolley of mass $m$ moving at a velocity $v$ along a smooth horizontal plane. It is full of water, and water is leaking at a constant rate out of the bottom of the trolley, i.e ...
3
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1answer
42 views

Particle sliding down frictionless hemisphere on frictionless surface

http://web.physics.harvard.edu/uploads/files/undergrad/probweek/prob87.pdf http://web.physics.harvard.edu/uploads/files/undergrad/probweek/sol87.pdf The problem and the suggested solution are in the ...
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Show that an isolated photon cannot undergo pair production [duplicate]

I need to see the mathematical details as how the conservation of four momentum is violated.
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0answers
22 views

Does inelastic collision mean the colliding particles have to necessarily stick?

In a case when particle 1 is moving vertically upwards and particle 2 if moving horizontally and they collide perfectly inelastically, why would the particles stick ? Since inelastic collision means ...
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2answers
45 views

When a ball bounces on a wall at an angle, why does the angle of incidence equal angle of reflection?

When a ball is thrown to a wall without spin and bounces, supposing it's an elastic collision, why does the angle of incidence equal the angle "reflection" (relatively to the normal), why isn't it any ...
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2answers
50 views

Why do $\hat{X}$ and $\hat{P}$ have to correspond to position and momentum?

As far as I understand, in QM we treat observables as operators, and the eigenvalues of these operators are the possible values we can measure of the observables. It is usually simpler to work in the ...
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1answer
21 views

What causes the skidding of the wheels of a moving car? Momentum or inertia?

In a moving car, when brakes are applied suddenly the wheels skid.I have these two explanations in my mind and both seems correct to me.1. The momentum of the car must be conserved so the car ...
2
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1answer
44 views

Nail clippers and conservation of momentum

As I clip my fingernails using nail clippers, pieces of nails sometimes fly off violently, reaching the other end of the room. What's happening in terms of conservation of momentum, how are the pieces ...
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1answer
86 views

conservation of momentum? [closed]

At hyperphysics I got this image, with the same description in text as is in this image It says that when a massive particle (say $A$) moving with a velocity collides with an object having a ...
2
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1answer
298 views

Particle In a box, momentum, and velocity

On a homework assignment, we are give the width of a well $a$, the mass of the particle $m$, and we want to find the average velocity of the particle at the $n=1$ state. Here is my attempt at the ...
2
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1answer
61 views

Is $E = p^0$ in non-inertial frames?

In special relativity the energy of a particle is the 0-component of the 4-momentum. However, is this still true in non-inertial frames, and in particular in non-freely-falling frames in general ...
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2answers
26 views

Why the speed of a cart stays the same, on a frictionless surface, as the sand falls out? [closed]

This is a question on my test. I got it right by guessing. Can someone explain it, in terms of equations of momentum. I first thought of the equation of conservation of momentum: ...
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1answer
74 views

Mathematical proof of an electron cant absorb a photon [duplicate]

How can we mathematically prove that a free electron cant absorb a photon totally?
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163 views

Portal 2 physics - one moving portal [closed]

A problem is posted and solved so many times on 9gag - till yet no good answer. The problem: you have two portals (one moving and one still standing). The one moving reach a still standing cube: what ...
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Calculating force of impact

Since $\text{force = mass}\times\text{acceleration}$, is it right to say that an object traveling at a high constant velocity (zero acceleration), exerts zero force upon impact with a stationary ...
2
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3answers
2k views

Conservation of 4-momentum in special relativity

I understand that the inner product of two 4-vectors is conserved under the Lorentz transformations, so that the absolute value of the four momentum is the same in any reference frame. This is what I ...
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2answers
151 views

Multiple conservation of momentum in one [closed]

I am in a Grade 12 Physics course and my teacher gave this question for bonus marks, to be solved with only highschool concepts. I suspect that this problem has to do with conservation of momentum, ...
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1answer
43 views

Four momentum in particle physics

I have seen four momentum defined in two different ways. One is $P =(E,\vec{p}c)$ and the other is $P =(E/c,\vec{p})$. Which one is correct and if they both are then why and when is it more convenient ...
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1answer
258 views

difference between magnetic dipole moment and torque on a magnetic dipole?

I am a bit confused. What is the difference between magnetic dipole moment and torque on a magnetic dipole ?
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70 views

How does the uncertainty principle make sense of the fact that momentum for massive particles depends in part on position?

The momentum of an object is in part dependent on the change in position meaning the final position minus the initial position. The equation for momentum is $$p=\frac{m \Delta x}{t\sqrt{1-(\Delta ...
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1answer
45 views

Lorentz covariant completeness relation

Let be $$ P^\mu |p> = p^\mu |p> $$ i.e. $|p>$ is the eigen-vector of the 4-momentum operator. Where does the following Lorentz-covariant completeness relation come from? $$ \int d^4p ...
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1answer
56 views

two object connected by a spring : momentum/energy topic [closed]

Here is my question below: Question Two objects A and B, connected by a light elastic spring with elastic constant 5.0 N/m, are initially at rest. The mass A is 2.0 kg and the mass B is 1.0 kg. ...
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2answers
102 views

Violation of the Newton's first law of motion in the movement of spacecrafts in the vacuum of space [closed]

Suppose a rocket at rest in space where there is a complete vacuum and no force to influence the rocket: In the left we have the rocket with a metal ball in it. After the ball is thrown out of the ...
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0answers
55 views

Is my expansion of the state $| x \rangle$ correct? [duplicate]

In my quantum mechanics textbook it says that the relation between the basis $|x\rangle$ and $|p\rangle$ is given by: $\langle p | x \rangle = \Large \frac{e^{-ip x/ \hbar}}{\sqrt{2\pi \hbar}} \, .$ ...
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1answer
39 views

mass attached to spring rotates in a horizontal circle [closed]

So here is the question I have: A mass of 2kg rotates at 1m/s in a horizontal circle on a table at the end of a spring with an elastic constant of 50N/m. If the original length of the spring is 2 ...
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73 views

Why Velocity is referred as momentum? [closed]

In many text books the velocity is referred to as a linear momentum which is being convected. For example the table in the following page My old conception is that the momentum or more precisely ...
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2answers
97 views

Why does Conservation of Momentum fails because of friction? [closed]

I did this experiment in my lab. We had two cars with wheel connected by a string. One car has a spring that can be triggered by a switch at the top of the car. (Frictionless surface and light string$ ...
3
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2answers
72 views

Mechanics impulse related

A bead of mass 'm' is connected at one end of an inextensible massless string. The other end of the string is fixed to a fixed cylinder. An initial impulse J is given to the bead perpendicular to ...
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0answers
11 views

Relativistic particle decay in ZMF [closed]

This is a problem that I feel is harder than I am making it but say you have: A particle at rest of mass $M$ decays into two smaller particles of masses $m_1, m_2$ where $m_1 \neq m_2$ and $M > ...
3
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3answers
101 views

Conservation of Momentum

Conservation of momentum can be derived during collisions by using Newton's laws of motion. But in other cases, do we simply take it like an axiom ?
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Comoving and physical momentum in a Friedmann universe

It is most probably a very basic question, but I'm a bit stuck with it. Let us consider a spatially flat Friedmann universe with the usual metric ...
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2answers
161 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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1answer
253 views

Fourier Transforms of position and momentum space in Quantum Mechanics

Fourier transformations: $$\phi(\vec{k}) = \left( \frac{1}{\sqrt{2 \pi}} \right)^3 \int_{r\text{ space}} \psi(\vec{r}) e^{-i \mathbf{k} \cdot \mathbf{r}} d^3r$$ for momentum space and ...
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2answers
55 views

Conservation of linear momentum (classical mechanics and special relativity)

How did Newton deduce the law of conservation of linear momentum? Can it be derived only by Newton's laws, or does it follow from practical experiments? If the law of conservation of linear momentum ...
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1answer
47 views

How do momentum get transferred?

Simple Question , Consider two objects namely $A$ and $B$ where $B$ is stationary and $A$ is moving towards $B$ with velocity $v$. When the two objects touch each other what does actually happen ...
5
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1answer
221 views

How does one account for the momentum of an absorbed photon?

Suppose I have an atom in its ground state $|g⟩$, and it has an excited state $|e⟩$ sitting at an energy $E_a=\hbar\omega_0$ above it. To want to excite the atom, one generally uses a photon of ...
5
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5answers
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Newton's second law of motion in terms of momentum

I am reading a document and in answer to the question State Newton’s second law of motion the candidate answers that The force acting on an object equals the rate of change of momentum of the object. ...
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2answers
308 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 ...