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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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 ...
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71 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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Why can we model a body to have a center of mass?

I accept that bodies have a center of mass. I also accept that if I were to suspend a body by only supporting it at its center of mass, then the body wouldn't rotate. In the scenario that we suspend a ...
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136 views

Massless particle that have momentum not equal to 0

I saw some problems in special relativity that use conservation of total energy and momentum and the conclusions are spectacular. My problem is the following: how can a massless particle like neutrino ...
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95 views

Moving objects using light

Photon do not have mass but they have momentum, can we use laser to pick up golf ball and hurl it several yards away without burning it into crisp?
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317 views

Difference in “momentum” names in Lagrangian mechanics

In the context of Lagrangian formulation of classical mechanics, the following names keep occurring in most textbooks, which confuse me a lot, are they different in any way? Momentum Generalized ...
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189 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, ...
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129 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 ...
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What are the general solutions to a hard sphere collision? [duplicate]

Surely someone has found the solutions to the hard sphere collisions (in $n$ dimensions) of two bodies of mass $m_1$ and $m_2$, respectively--that is the resultant velocities (or momenta) of the two ...
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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 ...
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582 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 ...
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25k 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?
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563 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 ...
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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 ...
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703 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 ...
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465 views

Rocket drive and conservation of momentum

I am currently reading through some lecture notes of Physics 1 and in a chapter about the dynamics of the mass point, there is an example covering the rocket drive. Let $v$ be the velocity of the ...
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845 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 ...
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62 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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75 views

Why is it easier to drop on to a downslope?

On a bicycle, why is it easier to land from a drop or jump on a slope going downwards than landing on a flat surface or on an upslope? I've already heard answers such as "because that's how a bike ...
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157 views

What's faulty in my reasoning about energy and momentum in this problem?

The question (from Sparknotes SAT Physics): An athlete of mass 70.0 kg applies a force of 500 N to a 30.0 kg luge, which is initially at rest, over a period of 5.00 s before jumping onto the ...
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278 views

Momentum change of a photon upon diffraction at a grating

How is the momentum change of a photon is related to the grating periodicity and diffraction order? I came across with this question while studying surface plasmon polaritons (SPPs) and how to excite ...
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142 views

Mathematical Proof of Force

I remembered reading an paper a while ago which tried to prove whether force actually exists, or if it a man made construct to aid our understanding of the world. However, I can't seem to find the ...
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371 views

Does the velocity vector always point in the same direction as the momentum vector?

I was told that the angular velocity vector does not always have to point in the same direction as the angular momentum vector. This is due to the fact that they are related by the equation $L=I ...
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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 ...
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Atmospheric pressure's effect on sound

An argument has been travelling in amongst my friends around this matter and after listening about it for 3 whole days I decided to ask it here. The Question is: Would a high atmospheric pressure ...
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67 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 ...
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Hermitian Adjoint of differential operator

I came across this equation (identity) (Eq. 4 in this paper): $\int(-i d\psi/dx)^*\psi dx = \int \psi^*(-i d\psi/dx) dx + id(\psi^*\psi)/dx\mid_{-\infty}^{+\infty}$ I have trouble proving it. I ...
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687 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 ...
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169 views

Is the reaction force for a stone hitting a wall infinite?

Let us assume a rigid stone which moves in empty space with a constant speed of $v$. (Or in the air with no friction and drag or you can imagine a free fall with friction). This stone hits a rigid ...
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106 views

A question regarding collisions

Let us consider a system of 2 identical spherical bodies connected by a massless string that is taut. If one body is placed at the origin then the other is placed at some coordinate $(x,y)$. The ...
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142 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 ...
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201 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 ...
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244 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: ...
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540 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 ...
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139 views

How does a “hammer thrower” that we see in the Olympics, impart so much momentum

How does a "hammer thrower" that we see in the Olympics, build so much momentum into the club? It's sort of like the golf swing, the more momentum, primarily in the club head, the further the ball ...
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224 views

How is the Principle of Conservation of Momentum proven using the Momentum-Impulse Principle?

Consider two particles moving in the same direction on the same line, $A$ and $B$, with mass $m_A$ and $m_B$, respectively. They also have velocies $u_A$ and $u_B$. They collide. After the collision A ...
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Bat hitting a ball

When a bat hits a ball, consider two cases: 1) The batsman goes for a defense, and stonewalls it, to reduce its speed. 2) the batsman goes for a shot, e.g. a home-run, etc. in which case will the ...
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Do photons actually generate a slight kinetic force?

My question is even though photons have no (rest) mass, do they emit a external force due to EM radiation causing electrons to be excited and jump to higher energy shells which electrons have mass ...
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91 views

When are energy, mechanical energy, momentum, and angular momentum conserved?

I am in AP Physics and my only real hangup is knowing when the said quantities are conserved. Please define what is the SYSTEM in your answer. I kind of have the basic idea. For example, if there ...
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62 views

Does third law of motion apply to light or EM waves? [duplicate]

Third law of motion - "For every action there is an equal and opposite reaction" I was considering the situation, where I may be motionless in space with only a flashlight and no forces acting on me. ...
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218 views

Why does the rule that elastic collisions are at 90 degrees in 2 dimensions not apply?

When one object collides with another object of the same mass in a 2D plane, we know that we can derive that the angles that the objects leave the collision at add up to 90 degrees in a perfectly ...
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Justification of $P_{\text{photon}}=E/c$ in derivation of $E=mc^2$

I recently was reading up on the derivation of $E=mc^2$. Now, I came across this derivation at this link. I noticed that several lines into the derivation they throw in the equation ...
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What am I REALLY doing when I take the Fourier transform of the momentum operator

I was playing around with some equations and found a surprising relationship when I took the fourier transform of the momentum operator Define $\hat P = \frac{\hbar}{i} \partial_x$, then $F(\hat P) = ...
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57 views

How can solar sails be maneuvered?

Photons from the Sun are always radial to it and hence solar sails can only travel radially. Any techniques related to maneuvering?
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404 views

Dumbbell rotation

What if apply impulse to dumbbell consisting of two masses and massless rod? It is clear for me that left dumbbell will move straight line. But it is not clear for me what kind of motion will have ...
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75 views

How are momentum and position operators dependent on the chosen inertial frame?

How are momentum and position operators in quantum mechanics dependent on the chosen inertial frame of reference?
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521 views

Elastic collisions and conservation of momentum

If you have an elastic collision between objects 1 and 2 and where 'kinetic energy is conserved', does this mean object 1 will always have the same velocity it had before the collision? Or will ...
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802 views

Will I be able to push a small object in front of me in the outer space?

Imagine I am standing on Earth, and pushing a tennis ball away from me. The ball moves. If it is very heavy, I will move back instead of the ball. Now consider the same scenario in outer space, where ...
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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?
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367 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 ...