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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What causes more damage, a head-on car crash at 30km/h or one car at 60km/h crashing into a stationary one?

Which will cause a greater impact? Two identical cars colliding head on (in opposite directions), each going at 30km/h OR One car travelling at 60km/h colliding into a stationary car (for the ...
-5
votes
1answer
55 views

Would this ship travel faster than light [on hold]

Im curious about using a geometric thruster system to break the speed of light barrier, Using a system of beams that rotate along alternating axis' from either end of themselves so as to travel a ...
2
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1answer
49 views

Relationship between position and momentum matrix elements

I am going through Faist's Quantum Cascade Lasers book. In the first section of the fourth chapter, he asserts that (in the context of a perturbative analysis of electronic transitions) the ...
1
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2answers
60 views

Question regarding elastic collisions and the conservation of momentum / energy [on hold]

I've been working on this question for a few hours and I cannot quite convince myself that my answer is correct. I've read the relevant section in my textbook, but I guess the lightbulb just isn't ...
0
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0answers
11 views

How do rockets fly? [duplicate]

Is it that when a rocket loses its mass due to the escaping gases that results in its acceleration due to the same force acting upwards? If so, how is Newton's Third Law associated with it?
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1answer
55 views

Using the momentum-space definition of the position operator in position space?

For the position operator $\hat X$: $\hat X \rightarrow x$ in position space $\hat X \rightarrow i \frac{\partial}{\partial k_x}$ in momentum space Question: Can $\hat X \rightarrow i \frac{\...
-3
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0answers
43 views

Movement of a box containig a particle [on hold]

A small thought experiment: Imagine a rectangular box in space, containing particle, all resting at $t=0$ from your point of view. At some point in time $t>0$ the particle starts to move with ...
0
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0answers
12 views

Movement of a bobbin thread when pulling it's thread at certain angles [closed]

The problem: You try to move a bobbin thread by pulling it by it's thread. If you pull it while the thread is horizontal it slides your way but if it is at an angle the bobbin thread starts rolling ...
0
votes
1answer
56 views

Conservation of enegry in case of Exploding Projectile [closed]

Consider the following problem : A projectile of mass M explodes, while in flight, into three fragments. One fragment of mass $m_1 =\frac12 M$ travels in the original direction of the projectile. ...
1
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1answer
68 views

De Broglie wave length of electron [closed]

Consider an electron with total energy $E>V_2$ in a potential well with $$V(x)= \begin{cases} \infty & x< 0 \\ V_1 & 0< x< L \\ V_2 & x>L \end{cases} ...
0
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1answer
28 views

Does a counterweight eliminate recoil/counter-torque?

A long, long time ago, I remember reading some scifi book that involved catapults whose throwing arm had a counterweight at the other end, such that the arm was balanced. The counterweight was not ...
1
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3answers
43 views

Where did 2mv come from in the solution to the question below?

I know that this is an inelastic collission, which is why the two objects have the same final velocity. However, I don't understand why they equated the V1(M+m) to 2mv. Where did they get 2mv from?
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2answers
38 views

Total Linear Momentum Conserved for Earth-Sun System? [closed]

According to 'Introductory Astronomy and Astrophysics' by Smith and Jacobs the total linear momentum of an isolated system is constant which they choose as zero, so they get (mv)1 = (mv)2. When I ...
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2answers
47 views

Why is momentum conserved in a control volumen?

I know momentum is conserved in an isolated system wherein there in not mass nor energy flow and the net resultant external forces are equaly to zero. My doubt is when I'm studying a (fixed) constrol ...
2
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2answers
67 views

Does a wave have inertia?

In de Broglie hypothesis, particles have wave nature. The question is does this wave have inertia? If so is it represented in the corresponding wave equation?
-1
votes
1answer
40 views

Mass ejection to improve trajectory?

Let me start with an example: Suppose I have a long range two stage rocket in pursuit of an agile aircraft of some sort. Once the fuel in the first stage is exhausted it may need to be ejected. Do ...
17
votes
2answers
463 views
+100

trouble reconciling doppler shift for energy and momentum of light

[See late addition at bottom for what currently remains unresolved in this question.] I have seen the assertion in a couple of places that if you trap light in a reflective resonator, or any other ...
23
votes
5answers
3k views

How do we know that energy and momentum are conserved?

How do we know energy and momentum are conserved? Are these two facts taken as axioms or have they been proven by an experiment? This question has been in part addressed here: Conservation of ...
6
votes
1answer
117 views

Why doesn't the relativistic formula for momentum appear consistent with collisions?

The relativistic formula for momentum is $$p = \frac{mv}{\sqrt{1 - \dfrac{v^2}{c^2}}} \,.$$ In the following example, I apply the formula in the most basic way possible to the addition of velocities. ...
1
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1answer
51 views

Orbiting in space

Background I'm making a game where a spaceship needs to orbit another object in space at a set distance. Space is, unlike other game, like space is in reality. Friction less. (at least to my ...
-1
votes
1answer
41 views

Quantum vacuum thruster and conservation of momentum [duplicate]

I have been reading about the quantum vacuum thruster on Wikipedia and I think I understand the idea of virtual particles being created and destroyed but what I don't understand is how this is ...
1
vote
1answer
50 views

Two carts on a frictionless rail collide [closed]

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 ...
0
votes
1answer
84 views

Why is mass times position not used in physics? [closed]

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} \...
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2answers
158 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. ...
0
votes
1answer
47 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. ...
30
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4answers
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 ...
0
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2answers
85 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 ...
0
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0answers
22 views

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 ...
0
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0answers
58 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) $...
0
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1answer
48 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 ...
0
votes
1answer
100 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 ...
1
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4answers
80 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 ...
1
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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
72 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 ...
0
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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), \...
0
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0answers
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 ...
3
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0answers
50 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 ...
2
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1answer
48 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 ...
0
votes
2answers
84 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 ...
0
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1answer
131 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?
-2
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1answer
61 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 ...
0
votes
3answers
58 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. ...
4
votes
2answers
60 views

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 ...
12
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3answers
2k views

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. ...
0
votes
1answer
50 views

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, ...
0
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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
votes
2answers
96 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 ...
0
votes
1answer
49 views

Double Integrals of Force

I took AP Physics C and Multivariable Calculus last year, and noticed something interesting. For non-relativistic particles in one dimension:$$F=\frac{\partial p}{\partial t}=\frac{\partial E}{\...
0
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1answer
83 views

Eigenstates of position and momentum operators in QM

In Griffiths pages 103-105 "Introduction to Quantum Mechanics" 2nd editiion he states that the eigenfunctions of the position and momentum operators are $$g_y(x) = \delta(x-y)$$ where the eigenvalue ...
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 ...