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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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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4answers
763 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
2k 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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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 ...
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2answers
97 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
99 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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1answer
80 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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1answer
234 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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3answers
97 views

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 $$P_{\text{photon}}...
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2answers
188 views

Problem on electromagnetic induction and Newtonian physics

Please imagine a solenoidal toroid (i.e. a donut shaped inductor) powered by an AC voltage source. It creates a changing magnetic field which is confined to the interior of the toroid (i.e. within the ...
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1answer
117 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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58 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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417 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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1answer
79 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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527 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 ...
2
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2answers
901 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
106 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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1answer
381 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 ...
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3answers
532 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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1answer
106 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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3answers
1k 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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2answers
1k 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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1answer
809 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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669 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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1answer
338 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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247 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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243 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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1answer
56 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 ...
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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 ...
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1answer
55 views

Simple frame of reference problem (conservation of momentum?)

I'm having trouble wrapping my head around a particular concept. Suppose we have a machine that fires balls of speed $u$ at some mass rate $\sigma$ (of units $\frac{kg}{s}$) directly at a car of mass $...
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3answers
175 views

Derivation of $E=pc$ for a massless particle?

In classical mechanics, massless particles don't exist because for $m=0$, $p=0$. The relativistic relation between energy, mass and spatial momentum is: $E^2= (pc)^2 + (mc^2)^2$ . So it is said that ...
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1answer
167 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$\...
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171 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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1answer
151 views

What's the physical meaning of change in momentum vector?

If I there is a initial momentum of 10Ns upwards, and final momentum of 10Ns to the right, I can find the difference in momentum by drawing a triangle and finding the resultant vector. But, how is ...
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1answer
42 views

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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1answer
156 views

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 ...
2
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1answer
152 views

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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2answers
235 views

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 ...
2
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1answer
116 views

Calculating speed of spheres in an asymmetric Newton's cradle?

If we assume there is an asymmetric Newton's cradle with 3 spheres of different masses and the first one is initialized with some certain speed can we calculate the outcome speed of the all the three ...
2
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1answer
200 views

What would happen if Newton's Cradle was made of other geometrical objects rather than spheres?

What would happen if Newton's Cradle was made of other geometrical objects rather than spheres? For example, what would happen if it was made of cubes and the contact area was larger?
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1answer
374 views

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 ...
2
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1answer
54 views

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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4answers
202 views

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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1answer
90 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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2answers
377 views

Symmetries of a Uniform Magnetic Field

Simple question. A system with a uniform electric field everywhere in space has translational invariance in the directions perpendicular to the electric field but no translational invariance parallel ...
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2answers
5k views

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
9k views

Proof that the momentum operator is Hermitian

I am trying to prove that the momentum $p_x$ operator is Hermitian, my approach is the following $$<p_x>~=~\int \Psi^*(\vec{r},t)[-ih\frac{\partial}{\partial x}]\Psi(\vec{r},t)\, d^3r.$$ I try ...
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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 ...
2
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570 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 ...