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.

learn more… | top users | synonyms

3
votes
2answers
193 views

Why does a stationary force affect the conservation of momentum, but not the conservation of energy?

Let's say I have two positive charges approaching one another at the same speed with only their mutual forces acting on one another. Total momentum (= 0) and energy is conserved and the charges ...
3
votes
3answers
323 views

Where do the conservation laws come from?

I know the conservation of energy comes from Noether's theorem via the time-translational symmetry, and if I remember correctly, the conservation of momentum comes from space-translational symmetry. ...
3
votes
2answers
3k views

block slides on smooth triangular wedge kept on smooth floor.Find velocity of wedge when block reaches bottom

Find the velocity of the triangular block when the small block reaches the bottom: Here is what I did: The final velocity(at the bottom)of the small block of mass m is $\sqrt{2gh}$ along the plane ...
3
votes
4answers
795 views

Is the momentum operator well-defined in the basis of standing waves?

Suppose I want to describe an arbitrary state of a quantum particle in a box of side $L$. The relevant eigenmodes are those of standing waves, namely $$ \left<x|n\right>=\sqrt{\frac{2}{L}}\cdot ...
3
votes
1answer
3k views

How do kinetic energy and linear momentum relate?

It took me quite a long time to click my gears in place and even then I'm not sure it's completely correct. The problem is that I need to understand these concepts (physics concepts; not just these ...
3
votes
2answers
2k views

Quantum momentum (De Broglie)

The de broglie hypothesis suggests a particle can be associated with a wave of momentum $p = \hbar k$ my question is the following: how does one arrive at this concept of the momentum of a wave? I ...
3
votes
4answers
175 views

Definition of force, kinetic energy and momentum

I've edited the post. Q1 and Q4 are the important ones but I didn't delete Q2 and Q3 since some older answers would not make sense anymore. To begin with, the formula of the kinetic energy $T$ is ...
3
votes
3answers
199 views

Why is momentum quantized in a 1D box even though the operator doesn't give eigenstates?

We don't get eigenstates of momentum when we operate momentum operator in the wave function of particle in a 1D box problem yet we say momentum is quantized in this situation. Why is it so?
3
votes
1answer
122 views

Hamilton-Jacobi formalism and on-shell actions

My question is essentially how to extract the canonical momentum out of an on-shell action. The Hamilton-Jacobi formalism tells us that Hamilton's principal function is the on-shell action, which ...
3
votes
2answers
88 views

Identity in quantum operator tutorial

I'm reading this tutorial by Ben Simons entitled Operator methods in quantum mechanics in connection with his course in advanced QM, and I'm a bit puzzled by an identity in page 25, a bit above ...
3
votes
2answers
371 views

Origin of motion and relative speed of bodies in the universe

Charged particles can hit the earth at relativistic speeds. But it seems that all large bodies have fairly low relative speed. Of course, speed can increase considerably when a body orbits close to a ...
3
votes
2answers
195 views

Two-body problem questions

I am self studying the two body problem and I'm stuck on the following: I have given $$\ddot{\vec{x}}_1= - G m_2 \frac{\vec{x}_1-\vec{x}_2}{|\vec{x}_1-\vec{x}_2|^3}$$ and $$\ddot{\vec{x}}_2= - G ...
3
votes
2answers
255 views

Conservation of Linear Momentum at the point of collision

This is a pretty basic conceptual question about the conservation of linear momentum. Consider an isolated system of 2 fixed-mass particles of masses $m_1$ and $m_2$ moving toward each other with ...
3
votes
1answer
953 views

Walter Lewin Lecture 16 - Ball bouncing on wall?

I never did Physics in university and I consider that a mistake so I am correcting that now by teaching myself. To that extent I have been watching the MIT lecture videos by Walter Lewin and I am ...
3
votes
1answer
166 views

Interpretation of Conjugate Momentum in Field Theory

The conjugate momentum density, following as a conserved quantity with Noethers Theorem, from invariance under displacement of the field itself, i.e. $\Phi \rightarrow \Phi'=\Phi + \epsilon$, is given ...
3
votes
1answer
117 views

When a moving body collides with a stationary body, far from its centre, how do you calculate the resulting spin

Imagine you had a long heavy rod in space with no significant gravity acting upon it. And a projectile is flying towards it, perpendicular to the orientation of the rod, with the impact some between ...
3
votes
2answers
2k views

Why is momentum conserved when a ball hits a vertical wall?

Almost in every book on physics, there's an example of conservation of momentum when the ball that is moving horizontally in the air, hits some massive wall. They claim that the return speed of the ...
3
votes
1answer
457 views

Simple 2D Vehicle collision physics

I'm trying to create a simplified GTA 2 clone to learn. I'm onto vehicle collisions physics. The basic idea I would say is, To apply force F determined by vehicle A's position and velocity onto point ...
3
votes
4answers
2k views

Is it possible to lift yourself off from the ground?

Say for instance a person who was strong enough to lift double his body weight. If he placed his hands under his bottom and tried to lift$^1$ himself$^2$ off the ground, could he? -- $^1$In a ...
3
votes
2answers
131 views

“Dark” quantities

I don't know much about the so-called dark matter, apart from what has been described in popular descriptions of the reasons for it being postulated. My question is, is there dark momentum, dark ...
3
votes
0answers
49 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 ...
3
votes
0answers
157 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 ...
3
votes
0answers
89 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: ...
2
votes
2answers
1k views

Matter waves and de Broglie wave length

The wavelength of a particle of momentum p is calculated using De Broglie relation. The de Broglie relation was postulated for what is called a matter waves. Now according to the statistical ...
2
votes
1answer
384 views

What if exactly half the Earth's population jumped at one instant? + Secondary Question

I read somewhere that when you jump, the sole effect caused by your jump on the earth moves it about $10^{-18}m$ (I don't remember the figure exactly, but I think it was that). However - obviously ...
2
votes
2answers
187 views

A thought on definition of momentum

Well, this is a simple, basic and I think even silly doubt. The first time I saw the definition of momentum as $p = mv$ I started to think why this is a good definition. So I've read the beginning of ...
2
votes
3answers
653 views

Simple elastic collision

If a particle with mass $m$ collides with a wall at right angles, and the collision is perfectly elastic. The particle hits the wall at $v\ ms^{-1}$. There is no friction or gravity. So the particle ...
2
votes
2answers
29 views

Question relating to energy transfer in between two particles

How would I go about calculating the maximum kinetic energy transferred from one particle when it forms an elastic collision with another particle. For example, if I had two billiards one with mass m ...
2
votes
3answers
134 views

When is momentum not conserved?

What are some common examples where momentum is not conserved? This question arose in my mind when I read that a ball dropped from a height penetrates into a bed of sand and that momentum is ...
2
votes
1answer
59 views

Motivating the ansatz for the infinitesimal translation operator

I'm reading Sakurai's Modern QM right now and in the first chapter he states a number of conditions required for a translation operator: unitarity, ...
2
votes
4answers
133 views

What do you exactly mean when you say that momentum is conserved?

I am taking for granted that when we say that something is conserved it is understood 'in its full integrity'. Energy is represented by a number (of J, or other) and is usually conserved. But ...
2
votes
4answers
163 views

How to calculate a collision which is partly elastic and partly inelastic?

(For the purpose of this question, "calculating a collision" means: given the velocities and masses of two objects in a collision, figuring out the new velocities of both objects after the collision). ...
2
votes
1answer
69 views

Simultaneous conservation of linear and angular momentum

Suppose there is a ring in the space where there is no gravity. The width of the ring is $r$ which is negligible compared to its inner radius $R$. The ring is in horizontal position. Now imagine a ...
2
votes
2answers
195 views

Canonical momentum density vs. energy-momentum tensor

Suppose we have a scalar field $\varphi$ with Lagrangian $$ \mathcal{L} = \frac{1}{2} \kappa \left( \frac{\partial \varphi}{\partial x} \right)^2 + \frac{1}{2} \rho \left( \frac{\partial ...
2
votes
3answers
2k views

Why does rubber ball bounce back while iron ball doesn't?

Suppose there are two balls, one of rubber and the other metallic. There are of the same mass and are thrown on a wall with the same velocity. Why does a rubber ball bounce back while a metallic ball ...
2
votes
2answers
384 views

Does trade affect Earth's rotation? [duplicate]

Every country is trading with other countries around the world, some more than others. I was wondering if there would be any change to the Earth's rotation because of the imbalance of trade between ...
2
votes
1answer
277 views

How to get the new direction of 2 disks colliding?

I'm developing a 2D game including collisions between many disks. I would like to know how I can get the angle corresponding to the new direction of each disk. For every disk I have this information ...
2
votes
2answers
2k views

Do the physics in the FlyBoard video make sense?

If you haven't seen the video of the FlyBoard, please have a look: http://www.youtube.com/watch?v=Cd6C1vIyQ3w&feature=youtube_gdata_player Yes, it's amazing, but do the physics make sense or is ...
2
votes
3answers
443 views

Explanation for classic mechanics puzzle

I'm trying to figure out a nice way to describe to a kid the physics behind these experiments: Assuming ideal conditions, we have a small boat with a sale, close to a lake's shore and a fan fixed on ...
2
votes
3answers
488 views

Train crash: are these situations alike? [duplicate]

I was just wondering... I believe that if a car travelling 50 miles per hour crashes into a wall, the result should be the same as crashing to another car also travelling 50 miles per hour (but in the ...
2
votes
2answers
117 views

Momentum vector transformation

I am confused about the way momentum vector transforms in the following case: $$q_k \to q_k'= q_k + \epsilon f_k(q)$$ The Jacobian is thus $\Lambda_{ij} = \frac{\partial q'_i}{\partial q_j} \approx ...
2
votes
1answer
83 views

How to get the accurate relativistic momentum form for photons? [duplicate]

I have studied from Griffiths, the relativistic form of momentum is $$p = \frac{1}{\sqrt{1-\frac{v^2}{c^2}}} m_0v$$ Now when I evaluate the momentum for photon, I just insert $v=c$ and $m_0=0$ and I ...
2
votes
1answer
41 views

Work done or not in this case?

I have a very simple question. A motorboat directed upstream is seen to be at rest from the bank of a river. Is the engine doing any work? Is it right to say that since it is not causing any ...
2
votes
3answers
288 views

How does the solar sailing concept work?

Wikipedia describes solar sailing as a form of spacecraft propulsion using a combination of light and high speed ejected gasses from a star to push large ultra-thin mirrors to high speeds. I ...
2
votes
2answers
5k views

Small car colliding with large truck

A small car collides with a large truck. Why do both vehicles experience the same magnitude of force? Wouldn't the large vehicle experience less force than the small one?
2
votes
2answers
86 views

Where did the universe get its initial momentum?

If, according to Newton's third law, forces come in pairs then what about the big bang? where did the universe get that initial push/momentum?
2
votes
1answer
77 views

Does the average momentum vanish for an eigenstate of the simple harmonic oscillator?

Suppose we have a simple harmonic oscillator, let's consider the ground state, $|0\rangle$ and the first excited state $|1\rangle$. $\langle 0|\hat p|0 \rangle$ is zero right? Since the particle can ...
2
votes
3answers
163 views

Equilibrium that is not stable

Consider a system which is in an equilibrium state. Now, a small perturbation causes it to start oscillating about the equilibrium state, but over time, the momentum with which it overshoots the ...
2
votes
1answer
163 views

Why positronium can annihilate in vacuum?

I thought that the annihilation process of positronium cannot take place without a third-party particle. This can be directly derived from energy & momentum conservation: energy conservation: ...
2
votes
2answers
218 views

How to calculate velocities after collision?

I'm currently writing a program for a particle simulator. One of the requirements is that the particles collide in a realistic way. However, I don't know how to calculate the final velocities. For ...