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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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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286 views

Isolated and non-isolated systems: Momentum?

I'm having a difficult time understanding why two billiard balls colliding is an isolated system, yet a car crashing into a wall is a non-isolated system. Does it really only have to deal with the ...
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103 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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191 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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5answers
622 views

Is the canonical momentum conserved when a particle moves in magnetic field?

Here is a question about the canonical momentum that I had asked some days ago, but I still have one point that I am not understand. Considering a particle moves in a magnetic field with charge $q$ ...
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210 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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387 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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122 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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182 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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562 views

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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2answers
1k views

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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Finding final velocity in inelastic collision [closed]

Information: In a shipping company distribution center, an open cart of mass 49.0-kg is rolling to the left at a speed of 5.40-m/s (see the figure). You can ...
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87 views

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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52 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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70 views

Diffracted electron - where does it gain additional momentum?

When an electron is diffracted, the momentum after the diffraction has different direction than before. Where does the electron gain this momentum? This is related to this question, but it's ...
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51 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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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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2answers
294 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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2answers
100 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?
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732 views

How do the electric or magnetic fields contain momentum?

I have recently come to know that the electric and magnetic field contain both linear and angular momenta, which are known functions of the electric and magnetic fields at any given point in space and ...
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473 views

What are the general solutions to a hard sphere collision?

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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336 views

What happens with a tunneling particle when its momentum is imaginary in QM?

In classical mechanics the motion of a particle is bounded if it is trapped in a potential well. In quantum mechanics this is no longer the case and there is a non zero probability of the particle to ...
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99 views

Energy/Momentum required to deflect earth from its orbit

This question occurred to me when thinking about the firepower people have on earth. How hard is it to change the characteristics of the orbit of the earth when an explosion happens on its surface, ...
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Calculating angular velocity after collision

Suppose I have a disc which doesn't move, just rotate around the axis going through its centre of mass perpendicular to its surface. The disk has a stick perpendicular to its surface at the edge. I ...
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719 views

Steady isothermal flow of an ideal gas

So I have a steady isothermal flow of an ideal gas through a smooth duct (no frictional losses) and need to compute the mass flow rate (per unit area) as a function of pressures at any two different ...
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816 views

Conservation of linear momentum magnitude along a trajectory

I was once criticized for "taking angular momentum as momentum going in a circle". I was loosely trying to state, in classical mechanics, that in using conservation of momentum, one can switch between ...
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597 views

Quantum mechanical analogue of conjugate momentum

In classical mechanics, we define the concept of canonical momentum conjugate to a given generalised position coordinate. This quantity is the partial derivative of the Lagrangian of the system, with ...
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507 views

Single photon's effect on conservation of momentum?

When your looking at basic Compton theory you find that if you shoot a stream of photons at a particle (usually atoms or electrons), then you have the basic laws of conservation of momentum. The ...
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447 views

Fundamental properties of motion

The first paragraph of the Wikipedia article on the angular momentum operator states that In both classical and quantum mechanical systems, angular momentum (together with linear momentum and ...
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Elastic collision in two dimensions

Suppose a particle with mass $m_1$ and speed $v_{1i}$ undergoes an elastic collision with stationary particle of mass $m_2$. After the collision, particle of mass $m_1$ moves with speed $v_{1f}$ in a ...
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362 views

Displacement with zero velocity

I know that we can rotate a deformable object using internal forces only in space. Thus we can cause an angular displacement without the use of any external forces. The following youtube video shows ...
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282 views

Conservation of momentum with MOND

Assuming as true the phenomenological MOND law for low accelerations ($< 10^{-10} m s^{-2} = a_0$), and considering a small mass $m$ attached to a larger mass $M$ by a faint spring (let's think of ...
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236 views

Mass Shell in Light Cone Coordinates

I'm reading Zweibach's introduction to string theory, and don't understand one of his claims. He defined the mass shell to be the set of points in momentum space s.t. $p^2+m^2 = 0$. Then the physical ...
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237 views

Should any theory of physics respect the principle of conservation of angular momentum or linear momentum?

Is it possible that a theory that can describe the universe at the planck scale can violate things that we now consider fundamental in nature?For example can it violate rotational and translational ...
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69 views

Relativistic Lorentz Force with constant, perpendiuclar, and uniform E and B fields

I am trying to solve the following problem from the Fundamentals of Plasma Physics by Bittencourt (Problem 2.7): Analyze the motion of a relativistic charged particle in the presence of crossed ...
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How to pull out the momentum operator?

In the equation (1.7.17), how does operator $p$ get out of the bracket without any operation though $<a | $, $| x'>$ are function of $x'$? How to prove this?
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Doubt regarding stress-energy tensor definition

I'm having some trouble understanding the following definition of the stress energy tensor: $T^{\mu\nu}$ is the flux of four-momentum $p^{\mu}$ across a surface of constant $x^{\nu}$. Here's an ...
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Does constant velocity of center of mass imply linear momentum is conserved?

I know that if momentum is conserved for a system, you can derive that the velocity of the center of mass of that system is constant. I was wondering if the second condition also implies the first: if ...
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224 views

Conservation of linear momentum, when is it conserved?

Will Linear momentum be conserved in a non-inertial frame of reference? In other words what is the fundamental condition for linear momentum to be conserved? Also which is more fundamental- Newton's ...
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Total Momentum From a Standing Electromagnetic Wave

How does one show the momentum imparted to a perfect conducting resonance cavity (boundary) of any shape by a classical standing electromagnetic wave inside is zero? It should be by conservation of ...
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Swinging onto a Hill

I was just watching the movie "Frozen" (not the Disney one), and they were trapped in a ski lift 50 feet off the ground. They had to jump. My question is, when they jump, should they swing on the ...
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Losing mass in space

So I came across a question while studying laws of motion. Roughly, this is how it goes: There are two astronauts in a space shuttle, who together have mass 200 kg. If by doing exercise, they manage ...
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75 views

Relativistic fomulae for energy and momentum?

I know that the relativistic formulae for energy and momentum are: $E = \gamma mc^2$ and $\textbf{p} = \gamma m\textbf{v}$; Can we derive these formulae? If yes, where from?
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Conservation of momentum when friction is present

Conservation of momentum applies when net force is zero. Suppose that there is a system of a canon and a canonball. Total momentum of the system is zero before canonball is fired. Now canonball is ...
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1answer
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Heavy vs Light Particle Ideal Gases

Assume there are two ideal gases. The first is made of a light particle, and the second is made of a heavy particle. The two are of the same amount, in the same volume container, and at the same ...
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457 views

Two dimensional elastic collisions with varying angle of incident

If in an elastic collision I know all initial values and that mass for each object remains constant throughout the collision (but different from one another) how can I determine their final velocity ...
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547 views

Movement of man and ladder and their center of mass

Suppose there is a massless frictionless pulley. A rope over it carries a mass $M$ and on other side carries a ladder of mass $(M-m)$ and a man on that ladder, of mass $m$. Now the man starts ...
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341 views

Relativistic kinematics of particle decay

Suppose a particle decays to three other particles. The masses of all particles are assumed to be known and we work in the rest frame of the parent particle. So there are 12 parameters for this ...
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1answer
2k views

Finding force exerted in an Inelastic Collision

I did a lab today in Physics in which we launched ball from a spring loaded cannon directly into a pendulum that captured the ball, held it, and swung upwards with it (representing a totally inelastic ...
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momentum conservation question involving a rocket and a spaceship [closed]

With the engines off a space ship is cruising at a velocity of 230m.s It fires a rocket straight ahead at the enememy vessel. The mass of the rocket is 1300kg and the mas of the ship (not including ...