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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The Momentum Operator in QM

I've seen the 'derivation' as to why momentum is an operator, but I still don't buy it. Momentum has always been just a product $m{\bf v}$. Why should it now be an operator. Why can't we just multiply ...
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769 views

Conservation of Energy in Different Frames of Reference

Say I have a bucket of fuel that can produce 150J of energy by combustion. No matter what frame of reference an observer or the bucket of fuel is in, since the configuration of molecules stay the ...
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2answers
73 views

Mechanics impulse related

A bead of mass 'm' is connected at one end of an inextensible massless string. The other end of the string is fixed to a fixed cylinder. An initial impulse J is given to the bead perpendicular to ...
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116 views

Where does the equation $p=\frac{1}{c}\sqrt{T^2 +2mTc^2}$ come from?

Where does the relativistic formula $$p~=~\frac{1}{c}\sqrt{T^2 +2mTc^2}$$ come from? What is the derivation from Einstein's formula? $T$ is the kinetic energy $m$ is the mass $p$ is the momentum.
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888 views

Conservation of momentum and energy in an explosion

One simple problem is physics is to determine the mechanical energy difference after an explosion. To do this, you must assume that momentum is conserved because in a explosion you have internal ...
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129 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 ...
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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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586 views

Derivative of a Position Eigenket

I was flicking through Zettili's book on quantum mechanics and came across a 'derivation' of the momentum operator in the position representation on page 126. The author derived that ...
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Conservation of Momentum/Energy collision Problem

I'm working on a physics problem in preparation for the MCAT and there's this particular problem that's troubling me. I don't know if it's a bad question or if I'm not understanding some sort of ...
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4answers
271 views

Conservation of momentum in a baseball

Conservation of momentum: A thought experiment. A baseball is placed on top of a baseball holder, the kind used to train young batters. A batter hits the stationary ball perfectly horizontal, sending ...
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1answer
79 views

If a photon doesn't necessarily travel in a straight line, doesn't it defy the law of cons. of momentum?

I just finished reading Richard Feynman's lectures on Quantum Electrodynamics (QED: The Strange Theory of Light and Matter) and it fascinated me. However, there's an unanswered question I have from ...
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2answers
99 views

Can momentum be distributed to multiple objects which travel in different vectors?

This is a question about the conservation of momentum: If there were a cluster of billiard balls floating in space and the cluster was struck by one moving ball, the cluster balls would scatter in ...
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162 views

Where does the partial derivative come from in Sakurai's derivation of the momentum operator?

How is the momentum operator derived in Dirac formalism? I am reading Quantum Mechanics by Sakurai and he gives the following derivation. But I don't understand how he goes from the third equation to ...
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592 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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1answer
105 views

Special Relativity: Finding the Euler Lagrange of a massive particle

Knowing that $$\tag{1} L= -mc\sqrt{-\eta_{ab}\frac{d\xi^a}{d\lambda}\frac{d\xi^b}{d\lambda}}$$ we get $$\tag{2} p_a=\frac{\partial L}{\partial(d\xi^a/d\lambda)} = m\eta_{ab}u^b.$$ How come? If I ...
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340 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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1answer
249 views

Probability of measuring momentum [closed]

Suppose we have this wavefunction: $$ \psi = A \left( cos(kx) + cos (2kx) \right) $$ I have to find the possible results of measurement of momentum and their probabilities. Attempt For a momentum ...
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822 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 ...
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2k views

Can the velocity of the center of mass of two spheres change after a collision?

I'm curious as to whether or not the velocity of the center of mass of a system comprised of two spheres can change after the two spheres collide. Looking at the equation for the velocity of the ...
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2answers
281 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 ...
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3answers
422 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. ...
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165 views

Does spacetime have momentum?

In what sense can it be said that spacetime possesses momentum? Can an experiment be envisaged to test this question?
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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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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 ...
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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 ...
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101 views

Conservation of Momentum

Conservation of momentum can be derived during collisions by using Newton's laws of motion. But in other cases, do we simply take it like an axiom ?
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53 views

Conservation of linear momentum and velocity of a system (damper and spring in a series)

This example is from a book on dynamics. Let us consider the system above formed by two blocks (each of mass $m$) connected by a linear damper and spring in a series. They slide without friction on ...
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43 views

What is 'momentum outflow'?

Feynman, in his lecture, on Field momentum, used this term while relating the momentum of matter the field is interacting with & the field's momentum itself. Here is the excerpt: Just as the ...
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94 views

What happens when two bodies collide in a dynamics point of view?

I'm a high school student learning about energy and momentum. What confuses me is the things with elastic and inelastic collisions. I completely (in my opinion) understand those concepts in energy ...
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271 views

Estimate for energy dissipated by a damper/dashpot

I have a system with a mass $m$ attached to the end of a cable. The cable mass is assumed negligible. The cable is attached to the ground at the one end while the other, with the attached mass $m$, ...
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189 views

Is there difference in force when the height increases?

Consider a man with mass 50kg. When he jumps from a 2 meter height, the total force is $F=ma$ ie (mass * gravity), but nothing happens to him. When he jumps from a 50 meter height, the total force ...
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105 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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The elusive difference between force and impulse

Impulse is defined as the product of a force $F$ acting for a (short) time $t$, $J = F*t$, and that is very clear. What I find difficult to understand is how a force can exist that doesn't act for a ...
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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?
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How do I figure out the momentum of a water balloon when it reaches the person I am throwing it at?

Recently an experiment was performed in which myself and a partner filled a water balloon and threw it back and forth at each other without breaking it. We gradually increased the distance at which it ...
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1answer
177 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 ...
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100 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 ...
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748 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 ...
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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 ...
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76 views

4 momentum in particle physics, collision of positron and electron

If I have a positron striking an electron at rest to create 2 pions( + and -) and I want to calculate the minimum kinnetic energy that the electrons can possess to create these pions, then the created ...
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Why Does Angular Velocity Increase as Radius Decrease?

Suppose a child were to ask you why a tetherball (picture below) seems to speed up as it wraps around the pole. How would you explain this to them? Certainly you wouldn't say something like, "Angular ...
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382 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 ...
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186 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 ...
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550 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 ...
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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 ...
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“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 ...
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The physics of an anvil [closed]

I am trying to understand how an anvil might best be made. An anvil requires two essential characteristics: enough hardness to not be deformed under the blows of the hammer, but as little rebound and ...
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1answer
43 views

Particle sliding down frictionless hemisphere on frictionless surface

http://web.physics.harvard.edu/uploads/files/undergrad/probweek/prob87.pdf http://web.physics.harvard.edu/uploads/files/undergrad/probweek/sol87.pdf The problem and the suggested solution are in the ...
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Why Use the Non-Relativistic Momentum Operator in Relativistic Quantum Mechanics?

In deriving the Klein Gordon equation one starts out with the relativistic energy relation E^2 = p^2 + m^2 and substitutes the quantum momentum operator that corresponds to non-relativistic QM, p = -i ...
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What is the effective electron mass in a plasma?

Is there a way to calculate the effective electron mass in plasmas? Effective electron mass is usually defined as varying from the vacuum electron mass in solid state physics. However, momentum ...