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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If photons have no mass, how can they have momentum?

As an explanation of why a large gravitational field (such as a black hole) can bend light, I have heard that light has momentum. This is given as a solution to the problem of only massive objects ...
13
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5answers
2k views

How can there be net linear momentum in a static electromagnetic field (not propagating)?

I understand from basic conservation of energy and momentum considerations, it is clear in classical electrodynamics that the fields should be able to have energy and momentum. This leads to the usual ...
8
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5answers
937 views

Elastic collision of point particle and rod

A 1 meter long rod on the ice with mass $m_2=1$ kg is perpendicularly hit on one end by a point particle with mass $m_1=0.1$ kg. The collision is elastic and the point particle is bounced back in ...
6
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9answers
18k views

How can momentum but not energy be conserved in an inelastic collision?

In inelastic collisions, kinetic energy changes, so the velocities of the objects also change. So how is momentum conserved in inelastic collisions?
14
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4answers
1k views

Force as change in momentum vs. change in velocity

Is there ever a situation where the distinction between $F = m \frac{dv}{dt}$ and $F = \frac{dp}{dt}$ is important? I can't think of a situation where one is true and not the other (assuming only ...
14
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8answers
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Does leaning (banking) help cause turning on a bicycle?

I think it's clear enough that if you turn your bicycle's steering wheel left, while moving, and you don't lean left, the bike will fall over (to the right) as you turn. I figure this is because the ...
6
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1answer
2k views

Momentum as Generator of Translations

I understand from some studies in mathematics, that the generator of translations is given by the operator $\frac{d}{dx}$. Similarly, I know from quantum mechanics that the momentum operator is ...
4
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4answers
837 views

How does the momentum operator act on state kets?

I have been going through some problems in Sakurai's Modern QM and at one point have to calculate $\langle \alpha|\hat{p}|\alpha\rangle$ where all we know about the state $|\alpha\rangle$ is that ...
4
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2answers
613 views

Why is the “canonical momentum” for the Dirac equation not defined in terms of the “gauge covariant derivative”?

The canonical momentum is always used to add an EM field to the Schrödinger/Pauli/Dirac equations. Why does one not use the gauge covariant derivative? As far as I can see, the difference is a factor ...
2
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1answer
1k views

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 ...
0
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1answer
4k views

Violation of Newton's 3rd law and momentum conservation [closed]

Why and when does Newton's 3rd law violate in relativistic mechanics? Check this link.
10
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1answer
586 views

Neutrino Oscillations and Conservation of Momentum

I would like to better understand how neutrino oscillations are consistent with conservation of momentum because I'm encountering some conceptual difficulties when thinking about it. I do have a ...
3
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2answers
531 views

Rocket/Thrust/Gas/Free Expansion of Gas

We know, the rockets in space use Newton's 3rd law to increase their velocity and hence move. What I don't understand is how it is possible in space aka vacuum-state without air? From what I know, ...
1
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4answers
1k views

Can momentum be conserved in a perfectly elastic collision?

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 scalar J, and is conserved in elastic collision. momentum ...
62
votes
7answers
10k views

Can we theoretically balance a perfectly symmetrical pencil on its one-atom tip?

I was asked by an undergrad student about this question. I think if we were to take away air molecules around the pencil and cool it to absolute zero, that pencil would theoretically balance. Am I ...
11
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8answers
5k views

What is a rocket engine thrusting against in space?

I know Newton's third law of motion might be the answer for this but still I am wondering how the rockets could thrust in the empty space and move in the opposite direction. I guess an astronaut ...
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2answers
1k views

Photon energy - momentum in matter

$E = h\nu$ and $P = h\nu/c$ in vacuum. If a photon enters water, it's frequency $\nu$ doesn't change. What are its energy and momentum : $h\nu$ ? and $h\nu/c$ ? Since part of it's energy and momentum ...
5
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3answers
815 views

Does the canonical commutation relation fix the form of the momentum operator?

For one dimensional quantum mechanics $$[\hat{x},\hat{p}]=i\hbar $$ Does this fix univocally the form of the $\hat{p}$ operator? My bet is no because $\hat{p}$ actually depends if we are on ...
6
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2answers
5k views

What is p_T? (transverse momentum?)

I've been looking at a few papers in experimental physics (from the ATLAS collaboration, for example) and I've often run across phrases such as "high-p_T electron." What exactly is p_T? Is it simply ...
6
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4answers
2k views

Intuitive explanation of why momentum is the Fourier transform variable of position?

Does anyone have a (semi-)intuitive explanation of why momentum is the Fourier transform variable of position? (By semi-intuitive I mean, I already have intuition on Fourier transform between ...
5
votes
2answers
16k views

Difference between momentum and kinetic energy

From a mathematical point of view it seems to be clear what's the difference between momentum and $mv$ and kinetic energy $\frac{1}{2} m v^2$. Now my problem is the following: Suppose you want to ...
1
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2answers
12k views

Perfect elastic collision and velocity transfer

So my teacher told me that when you have two identical balls in a perfectly elastic collision, the first ball A will collide with B and afterwards A will stop and B continue. Why is this? Doesn't ...
2
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3answers
303 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 ...
2
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2answers
470 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 ...
1
vote
1answer
148 views

Where can I find the equations for “quasi” elastic collisions?

Yes, you all talk about neutrinos and spins, but I came out with this basic s**t :D All of us learnt the basic equations of collisions, elastic (everything bounces and energy remains the same), or ...
21
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6answers
12k views

Newton's cradle

Why, when one releases 2 balls in Newton's cradle, two balls on the opposite side bounce out at approximately the same speed as the 1st pair, rather than one ball at higher speed, or 3 balls at lower ...
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6answers
1k views

Does Newton's third law apply to momentum or to forces?

I read all the previous answers concerning the 3rd law and I have seen that it is definitely not universal, (Edit: but conservation of momentum is. If it is not universal it should be not a problem to ...
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5answers
4k views

What is canonical momentum?

What does the canonical momentum $\textbf{p}=m\textbf{v}+e\textbf{A}$ mean? Is it just momentum accounting for electromagnetic effects?
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6answers
3k views

Conservation of momentum when rain pours into a wagon

Suppose a wagon is moving at constant velocity on a friction-less surface, and rain begins to fill the wagon. The net force on the wagon is zero, so momentum is conserved; as the mass of the wagon ...
8
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3answers
1k views

Intuitively Understanding Work and Energy

It is easy to understand the concepts of momentum and impulse. The formula $mv$ is simple, and easy to reason about. It has an obvious symmetry to it. The same cannot be said for kinetic energy, ...
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4answers
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Relativistic momentum

I have been trying to derive why relativistic momentum is defined as $p=\gamma mv$. I set up a collision between 2 same balls ($m_1 = m_2 = m$). Before the collision these two balls travel one ...
9
votes
4answers
24k views

Which is easier, pushing or pulling?

It is generally assumed, from a person's perspective, that pushing a cart is more easier than pulling one. But why? Is there any difference in terms of force required to achieve the same amount of ...
6
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3answers
1k views

How does $F = \frac{ \Delta (mv)}{ \Delta t}$ equal $( m \frac { \Delta v}{ \Delta t} ) + ( v \frac { \Delta m}{ \Delta t} )$?

That's how it's framed in my Physics school-book. The question (or rather, the explanation) is that of the thrust of rockets and how the impulse is equal (with opposite signs) on the thrust-gases and ...
9
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5answers
4k views

How to get the position operator in the momentum representation from knowing the momentum operator in the position representation?

I know that $$\tag{1}\hat{p}~=~-i\hbar \frac{\partial}{\partial x}~.$$ How can I get $$\tag{2}\hat{x}~=~i\hbar \frac{\partial}{\partial p}~?$$ I think this simple and I'm just over thinking it, ...
4
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2answers
466 views

What is the most general expression for the coordinate representation of momentum operator?

I have a question about deriving the coordinate representation of momentum operator from the commutation relation, $[x,p]= i$. One derivation (ref W. Greiner's Quantum Mechanics: An Introduction, 4th ...
3
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1answer
1k 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
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2answers
371 views

Does constraint for speed of Electric and magnetic fields violates Conservation of momentum or Newton's third law?

I'm just a beginner so bear with me. Consider two frames at rest wrt to each other separated by distance enough for light to take a minute or so. At a given instant we create two large dipoles by some ...
5
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5answers
17k views

Newton's second law of motion in terms of momentum

I am reading a document and in answer to the question State Newton’s second law of motion the candidate answers that The force acting on an object equals the rate of change of momentum of the object. ...
3
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3answers
182 views

How can the linear momentum can be understood physically?

Currently reading Classical Mechanics by Herbert Goldstein, and I'm trying to understand every concept physically. Speed can be understood physically, as the distance traveled within a certain amount ...
2
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3answers
454 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 ...
6
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3answers
732 views

Lorentz force in Dirac theory and its classical limit

It is well known that in Dirac theory the time derivative of $P_i=p_i+A_i$ operator (where $p_i=∂/∂_i$, $A_i$ - EM field vector potential) is an analogue of the Lorentz force: $\frac{dP_i}{dt} = ...
4
votes
2answers
691 views

Does a force really act on a body during a collision?

Consider two bodies A(black) and B(red) having equal mass. A is moving at a constant speed towards B, which is stationary. At certain point of time, they collide elastically, $\therefore u_{A}=v_{B}$ ...
4
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3answers
2k views

Why is momentum conserved in an inelastic collision and kinetic energy is not conserved? [duplicate]

We know that in an inelastic collision that total momentum of the system before collision equals the total momentum after collision. But total kinetic energy before collision is not equal to total ...
4
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1answer
1k views

Use the relative velocity formula to find v2f in terms of v1f?

Q: A $0.150\text{ kg}$ glider is moving to the right ($+x$) on a frictionless, horizontal air track with a speed of $0.80\text{ m/s}$. It has an elastic collision with a $0.300\text{ kg}$ ...
3
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3answers
6k views

Conservation of momentum but not kinetic energy in inelastic collisions

In inelastic collisions, the kinetic energy of the system is not conserved but the momentum is. Kinetic energy is: $0.5 \times \text{mass} \times \text{velocity}^2$. Momentum is: ...
3
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3answers
1k views

Newton's 3rd Law: How can I break things?

If I punch a wooden board hard enough and it breaks in two, has the board still exerted a force of equal magnitude on my fist? When the board breaks in two due to my force, the halves have a ...
3
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4answers
3k 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 ...
2
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0answers
140 views

The relationship between angular and linear momentum

Why is orbital angular momentum not 0 when spin and linear momentum are not collinear? Why can it be 0 when spin and linear momentum are parallel? Like in the example of a scalar field at rest ...
2
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2answers
750 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 ...
2
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1answer
646 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 ...