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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Two carts on a frictionless rail collide

There're 2 carts on a frictionless rail. Their masses are $4m$ and $2m$. (The carts are on the rail in this order). The first cart has a velocity of $v_1$. The first cart hits the second. Knowing that ...
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Why is mass times position not used in physics?

The momentum $\vec{p}=m \vec{v}$ plays a very prominent role in physics. Why is the same not true for the quantity $\vec{q}=m \vec{r}$? E.g. one can write angular momentum as $\vec{L} = \vec{r} \...
7
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1answer
47 views

Relationship between crystal momentum and true momentum

Most textbooks make it clearly that crystal momentum is not true momentum. However, in a lot of literature, crystal momentum is treated as true momentum. Here's two examples: Rashba spin splitting. ...
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3answers
4k views

What is momentum really?

Wikipedia defines momentum as in classical mechanics: In classical mechanics, linear momentum or translational momentum is the product of the mass and velocity of an object. However, an ...
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198 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 vector....
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2answers
1k views

Average Force vs Net Force

The F in $$Impulse = F*t$$ is said to be the average force. For a ball dropped vertically onto a horizontal surface, the average force, F, on the ball from the floor is: $$F = \frac{\Delta{p}}{t}$$ $$\...
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1answer
43 views

How to calculate the linear momentum on a dumbbell? [closed]

In this picture there is a dumbbell and a mass in motion that hits one of the masses of the dumbbell. Now the problem is I have to find the velocity of the CM and the rotational speed around the CM. ...
3
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1answer
792 views

Phonon Momentum

I am reading Charles Kittel's solid state physics and wondering what's the mechanism that neutron waves and photons can interact with phonons and the process obey the generalized momentum-energy ...
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48 views

How to understand the momentum operator in a exponential function? [closed]

What's the integral expression or matrix expression of the quantum parlance $$U\left( {x - \Delta {x_i}} \right) = \left\langle {x|\exp \left( { - i\Delta {x_i}P} \right)|U} \right\rangle ,$$ where $...
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2answers
83 views

Solar Sail Questions

I'm just looking for a good (better) analogy. How do massless photons put pressure on a surface especially when it's a mirror? Using the analogy of the wind (atmosphere) on a sail breaks down when I ...
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7answers
3k views

Ball flying towards me or me flying towards ball

Suppose a ball is flying towards me at a speed of 10m/s and that, on impact, I feel "x" amount of pain. If, instead, it was me flying towards the ball at the same speed, with all other conditions ...
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1answer
41 views

Collisions; Linear Momentum [closed]

Let's say we got a rough surface with friction and there are 2 blocks, the block of the left has initial velocity and will collide with the block of the right, which is in rest. Consider an elastic ...
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How can a lateral wind gust create a lateral acceleration for a flying object?

We had a lot of wind today and we weren't able to fly our drone with some friends If a quadrotor of mass $1kg$ flying along the positive $x$-axis at a speed of $4m.s^{-1}$, why would a wind gust ...
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0answers
47 views

Trouble following an argument about a rocket problem

This is from pages 32-33 of Physics for Mathematicians. A rocket + fuel system of mass $m(t)$ is moving along at velocity $v(t)$, with its fuel being ejected at the velocity (relative to the rocket) $...
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4answers
74 views

Does momentum increase with out of phase photons?

This paper speculates that the EM drive produces thrust with out of phase photons: http://scitation.aip.org/content/aip/journal/adva/6/6/10.1063/1.4953807 My question is this, do out of phase ...
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1answer
94 views

Is the Potential Energy just a bookkeeping device?

It is said that if the space is homogeneous then momentum is conserved. But I've been thinking in the following situation: Consider a parallel plates capacitor. In between the plates there is a ...
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0answers
43 views

Can the momentum of a system be spacelike?

For a particle, we always have $Eu=p$ where $u$ is the speed of the particle and correspondingly the momentum is always timelike. For a system of particles, if the potential energy is not considered ...
2
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1answer
68 views

Three connected balls

I'm stuck solving this problem with three small balls of masses $m$, $2 m$ and $3 m$ on a smooth table, connected by two equal, light inextensible strings as shown, and initially at the vertices of an ...
2
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2answers
122 views

How to explain the momentum exchange of two solid particles collision at molecular scale?

Here is my question: assume two solid sphere collided to each other in vacuum, at macroscopic, it can be explain by Newton's law. But at molecular scale, does the surface atoms touch to each other or ...
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5answers
148 views

If “For every action there is an equal and opposite reaction”, why does a gun not injure the shooter's hand?

If "For every action there is an equal and opposite reaction", why does a gun not injure the shooter's hand? Would not the "equal and opposite reaction" of firing a bullet be the kickback the shooter ...
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0answers
37 views

How can $\hat p = - i \hbar \partial_q$ be derived starting from the definitions of $\hat q$ and $\hat p$ in terms of creation/destruction operators? [duplicate]

Consider the position and momentum operators $\hat q$ and $\hat p$, defined respectively in terms of creation and destruction operators in the usual way: $$ \hat q = c (\hat a + \hat a^\dagger), \...
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41 views

Momentum flux through cylinder wall

A fluid flows through a hovercraft, is bended and the freejet has a certain velocity $c$ with which it flows after exiting the hovercraft / beeing bended. There's a pressure difference between under ...
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1answer
123 views

Is conservation of momentum and energy valid for non-inertial frames?

Conservation laws of momentum and energy are said to be the most basic principles of physics. Are they also valid for non-inertial frames, and in what way?
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2answers
82 views

If I throw or kick a ball, how much will the Earth move in the opposite direction?

I understand that for momentum to be conserved, if I throw a tennis ball (or kick a football) the Earth must move in the opposite direction to the ball. Obviously this is an infinitesimally small ...
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1answer
45 views

Collision/Crumpling problem possible solution mistake

This question is from Physics for scientist and engineers , Ohanian . Two automobiles of 540 and 1400 kg collide head-on while moving at 80 kmh in opposite directions. After the collision the ...
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0answers
47 views

Integrals of motion for a free particle

I'm struggling to understand the argument on p. 13 in Landau and Lifshitz that for a system with $N$ degrees of freedom there must be $2N-1$ integrals of motion. In particular, I can't understand ...
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1answer
130 views

Mathematical proof of an electron can't absorb a photon [duplicate]

How can we mathematically prove that a free electron can't absorb a photon totally?
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1answer
58 views

Newton's 2nd Law with Dirac Delta, as a way to derive the Ideal Gas Law

I'm trying to derive the ideal gas law from first principles, namely that a particle bouncing off a wall will exert a force on the wall. Newton's second law $F=\frac{dp}{dt}$ relates the force an ...
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1answer
129 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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1answer
165 views

The norm of the vector sum of two 4-momentum vectors before and after pair production

Two photons traveling along the x-axis (in a lab frame of reference) of different frequencies are about to collide. Their 4-momentum vectors are (h$\nu_1$/c , h$\nu_1$/c , 0, 0) and (h$\nu_2$/c , -h$\...
16
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3answers
404 views

Momentum of transverse waves on a string

In general, if a wave carries energy density $u$ with velocity $v$, it also carries momentum density $u/v$. I've seen this explicitly shown for electromagnetic waves and (longitudinal) sound waves. ...
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3answers
55 views

Can internal forces bring any change in momentum of the system?

Imagine a rectangular box placed at the tip of an iceberg; the box contains a man who can freely walk/jump/rotate inside the box. The man walks up to one of the corners of the box and starts jumping. ...
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153 views

Rolling Friction Problem

The handbrake of a vehicle of mass $1.5\ \mathrm{tonnes}$ completely fails while it is parked on a $30^\circ$ slope. It rolls $20\ \mathrm{m}$ down the slope before colliding with, and locking on to, ...
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2answers
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Heisenberg EOM for $\langle x \rangle$ in momentum eigenstate - where is my error?

Equation of motion for expectation value of a quantum particle in a momentum eigenstate: $$\frac{d}{dt} \langle x \rangle = \frac{1}{i h} \langle [x,H] \rangle$$ and since it's in a momentum ...
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3answers
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What are some phenomena that can not be described without the help of Newton's third law of motion? [closed]

What are some phenomena that can not be described without the help of Newton's third law of motion? All the phenomena I can think of can be explained with the help of Newton's first law or second law. ...
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3answers
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Matrix elements of momentum operator in position representation

I have two related questions on the representation of the momentum operator in the position basis. The action of the momentum operator on a wave function is to derive it: $$\hat{p} \psi(x)=-i\hbar\...
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2answers
286 views

Deriving the expectation of $[\hat X,\hat H]$

For a free particle of mass $m$, with Hamiltonian $$\hat{H} = \frac {\hat{P}^2} {2m},$$ where $$\hat{P} = -i \hbar \frac{\partial} {\partial x}.$$ The commutative relation is given by $$[\hat{X}, \...
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3answers
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What's wrong with this derivation that $i\hbar = 0$?

Let $\hat{x} = x$ and $\hat{p} = -i \hbar \frac {\partial} {\partial x}$ be the position and momentum operators, respectively, and $|\psi_p\rangle$ be the eigenfunction of $\hat{p}$ and therefore $$\...
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2answers
251 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 ...
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8answers
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Can we explain Newton's first law mathematically?

At constant speed there is no acceleration. $(f'(x)=v'=0=a)$ .If $a=0$ then $F=ma=0$ and therefore no force acts on the object so the object will continue in the same direction, if any. This is only ...
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2answers
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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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2answers
99 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
128 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 ...
3
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1answer
414 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 $$\psi(\vec{r}...
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2answers
185 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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Impulse of two different objects

I was running over a question, A collision occurs between particles A and B which are moving in opposite directions in the same straight line. The impulse on each particle in the collision is 2N.s, ...
2
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2answers
94 views

Newton's Cradle: why does it stay symmetric? [duplicate]

How is it that always the same number of balls leave at the other end in Newton's cradle. I understand that the momentum needs to be conserved, but as momentum is defined as p=m*v couldn't you have a ...
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1answer
24 views

Probability to measure momentum of a certain range (eigenfunctions and such)

At a certain point in time a particle of mass $m$ has the corresponding function (function of $x$) $$\psi(x)=\begin{cases}Nx \exp[-bx]~~&\text{for}& x\geq 0 \\ 0 ~~&\text{for}& x&...
2
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1answer
47 views

How can you find the impact necessary to change the direction of Earth's spin?

If an object the mass of the moon was to hit earth's surface at an angle that would be in the opposite direction of earth's spin, how can you find how much momentum the object needs to cause earth to ...
3
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5answers
194 views

Where does $\hat{P}\psi(x) = -i\hbar \partial_x \psi(x)$ come from?

It's a very basic question, where does the relation $$\hat{P}\psi(x) = -i\hbar \partial_x \psi(x)$$ for any square integrable $\psi(x)$ come into existence? Some texts I found states that the above ...