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 ...
25
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1answer
616 views

Best current bounds on nonconservation of momentum?

It's not straightforward to test conservation of momentum experimentally, and many experiments that seem like tests really aren't. For example, in a Newtonian system of identical particles that ...
16
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6answers
712 views

Is there a momentum for charge?

Since mass and charge behave similarly, so, just like center of mass, I define a point center of charge, that is defined by $$\vec r_{qm} = \frac {\sum{q_i \vec r_i}} {\sum{q_i}}$$ where $\vec r_i$ ...
16
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5answers
754 views

Conservation of Mathematical Constraints when deriving Energy and Momentum from $F=ma$

Background: Starting from $F = ma$, integrating with respect to time, and using basic calc, one can derive $\int Fdt = m (v_f - v_i)$ Starting from $F = ma$, integrating with respect to distance, ...
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5answers
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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 ...
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 ...
12
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4answers
946 views

Energy is actually the momentum in the direction of time?

By comparatively examining the operators a student concludes that `Energy is actually the momentum in the direction of time.' Is this student right? Could he be wrong?
11
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7answers
3k views

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 ...
11
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4answers
943 views

Can a particle have momentum without energy?

Can a particle have linear momentum if the total energy of the particle is zero? Even if a particle has a certain velocity, can its potential energy cancel out the kinetic energy as to add to zero ?
10
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1answer
483 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 ...
9
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4answers
18k 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 ...
9
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6answers
5k views

Who discovered momentum?

I read some text about momentum in Wikipedia, but I didn't find any information who discovered momentum. Is the momentum a philosophic principle?
9
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3answers
586 views

Could a fish in a sealed ball, move the ball?

If you had a glass ball filled with water, completely sealed and containing a fish, could the fish move the ball?
9
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1answer
292 views

Can a fly pierce itself onto a cactus needle?

Somebody on reddit posted a ridiculous picture today of a fly pierced onto a needle of a cactus: http://www.reddit.com/r/pics/comments/xarue/what_are_the_odds_of_this_accident/ Whilst the OP claims ...
8
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4answers
22k views

What is the relationship between kinetic energy and momentum?

I can't seem to figure out the relationship between $E_k$ and $p$ or $F$. I understand that the units are pretty different. But for example: A bullet with a mass of 10.0g is moving at the speed of ...
8
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4answers
1k views

Examples where momentum is not equal to $mv$?

I am aware that momentum is the thing which is conserved due to symmetries in space (rotational symmetry, translaitonal symmetry, etc). I am aware that in some systems, the generalized momentum, ...
8
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5answers
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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, ...
8
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2answers
370 views

Translation Invariance without Momentum Conservation?

Instead of the actual gravitational force, in which the two masses enter symmetrically, consider something like $$\vec F_{ab} = G\frac{m_a m_b^2}{|\vec r_a - \vec r_b|^2}\hat r_{ab}$$ where $\vec ...
8
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3answers
778 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, ...
8
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2answers
226 views

How multiple objects in contact are resolved in an inelastic collision, when edge normals don't “line up”

In a case I understand, let's say I have an object A moving at velocity V toward 3 objects in contact B, C, and D: The momentum of A is the mass of A times its velocity. To figure out how the ...
7
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3answers
9k views

How does the 'water jet pack' work?

So I was cruising around at YouTube and saw this sweet video, and as I was watching started to wonder: "How is this possible?". For a little bit of background, in case you decide to not watch the ...
7
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2answers
872 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 ...
7
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3answers
189 views

The elusive difference between impulse and momentum

1) In classical mechanics, impulse is the product of a force, F, and the time, t, for which it acts. The impulse of a force acting for a given time interval is equal to the change in linear ...
7
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2answers
662 views

What are the properties of two bodies for their collision to be elastic?

For example, must the shock wave in each body be of a particular form which influences the shape and material properties of the bodies? I suspect part of the the answer is that the objects must be ...
7
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9answers
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How to explain independence of momentum and energy conservation in elementary terms?

I'm trying to explain to someone learning elementary physics (16 year old) that linear momentum and energy are conserved independently. I'm not a professional physicist and haven't tried to explain ...
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3answers
841 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 ...
6
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2answers
263 views

About photons and mirrors

If a photon hits a 'perfect' mirror (with no environment interference) would the mirror move a bit?
6
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3answers
564 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} = ...
6
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2answers
204 views

Why $-i\hbar\vec\nabla$ for momentum in quantum mechanics, while $m\vec{v}$ in classical mechanics?

I am a little bit confused when thinking of the momentum representation in QM and CM. In QM, momentum is represented as $-i\hbar\vec\nabla$, while in classical, momentum is represented as $m\vec{v}$. ...
6
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1answer
407 views

Impact force in a fall

I'm a climber and I constructed myself an anchor that I fixed to a rock wall. To test it, I hooked to it a 12mm in section steel cable with a length of 2,8m and a concrete block of 30kg to the other ...
6
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1answer
96 views

In calculations with uncertainty principle why could you equate the uncertainty in momentum with the actual momentum of the system

This website is trying to calculate the confinement energy of a electron starting from the uncertainty principle, but it does this: $\Delta p=p$. Why is this valid?
6
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2answers
252 views

Proof for $p=\gamma_Pmu$

As I'm reading about Relativistic Momentum, my book states the following: $$p=m \frac{\Delta x}{\Delta t}=m\frac{\Delta x}{\sqrt{(1-u^2/c^2)}\Delta t}=\frac{mu}{\sqrt{1-u^2/c^2}}=\gamma_Pmu$$ ...
6
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3answers
128 views

Movement in outer space via Newton's law of every action has an equal and opposite reaction

What is more effective for travel in outer space ignoring all other factors like air radiation etc. I have a 10 kg bag of rice would I travel faster throwing the whole bag at once or throwing a grain ...
6
votes
1answer
148 views

Lorentz covariance of the Noether charge

The invariance under translation leads to the conserved energy-momentum tensor $\Theta_{\mu\nu}$ satisfying $\partial^\mu\Theta_{\mu\nu}=0$, from which we get the conserved quantity$$P^\nu=\int ...
5
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4answers
263 views

A question abou $E=pc$ for massless particles

Since photon has no (rest)mass and $$E^2=(pc)^2+(mc^2)^2$$ we derive that $E=pc$ for particle with no (rest)mass. However, if we transform the non-relativistic formula for kinetic energy ...
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7answers
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How does gravity affect bullets?

I read recently that if you hold a bullet in one hand and a pistol in the other, both hands at the same height, and subsequently fired the pistol at the same time as dropping the bullet, both bullets ...
5
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4answers
2k views

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 ...
5
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1answer
196 views

Why isn't $F = \frac{\partial \mathcal{L}}{\partial q}$?

If momentum is, $$p = \frac{\partial \mathcal{L}}{\partial \dot{q}}$$ and force is, $$ F = \frac{dp}{dt}$$ and by Euler-Langrange equations, $$ \frac{d}{dt}\frac{\partial \mathcal{L}}{\partial ...
5
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3answers
2k views

Is the giant Newton's cradle in the Kit-Kat ad feasible?

Apologies in advance if this is too basic a question for Phys.SE. I don't want to dumb down this venerable institution. :) My wife and I just watched this TV ad for Kit-Kat where a crew of crane ...
5
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4answers
457 views

How to tell if the collision is elastic or inelastic?

I'm a programmer and a game developer, not a mathematician or a physicist. So please go easy on the math :) I know two things: How to find the new velocities of two objects after an elastic ...
5
votes
5answers
14k 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. ...
5
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2answers
4k 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 ...
5
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2answers
11k 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 ...
5
votes
3answers
343 views

How can particles travel in a straight line?

A particle can be set off in a certain direction by giving them momentum. Momentum is a vector, so the particle heads off in a specific direction. But the wave function of the particle allows it to ...
5
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4answers
327 views

Can a balloon be used as an anchor point for a pulley?

For a physics/ engineering contest, I want to use a large balloon as an anchor point for a pulley. This would allow me to raise and drop masses. However, in testing, when I pull on the pulley the ...
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4answers
2k 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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3answers
4k views

What is the difference between impulse and momentum?

What is the difference between impulse and momentum? The question says it all...I know the second of of them is mass * velocity, but what is the first one for, and when is it used? Also, what are its ...
5
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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 ...
5
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3answers
3k views

Does conservation of momentum really imply Newton's third law?

I often heard that conservation of momentum is nothing else than Newton's third law. Ok, If you have only two interacting particles in the universe, this seems to be quite obvious. However if you ...
5
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2answers
119 views

Does a reflection still transfer momentum to an mirror?

I have been recently wondering, if I take a powerful enough energy source (photon) and I have an perfect mirror exactly in front of it and assume an "emitter" shot the light towards the mirror. As ...