Tagged Questions

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.

99k views

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 ...
12k 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 ...
6k views

Please forgive my lack of artistic ability, but here's my question: Consider that a skydiver, without using his parachute, were to fall exactly parallel to a giant curved slide that starts at $90\,^\... 3answers 8k views Can kicking a falling phone save it from shattering? So I saw this tip but I don't think this is true, it would be that your leg or shoe is more flexible than a hard floor so the momentum change would be slower right? 3answers 4k views What is momentum really? Wikipedia defines momentum as in classical mechanics: In classical mechanics, linear momentum or translational momentum is the product of the mass and velocity of an object. However, an ... 5answers 13k views Is it possible to shoot bullets in space or would the recoil of the gun be too strong? I've read a few articles that say that astronauts have already brought guns in space and that shooting bullets in space is possible. But won't the recoil of the gun be too strong? Law of ... 1answer 774 views Best current bounds on nonconservation of momentum? It's not straightforward to test conservation of momentum experimentally, and many experiments that seem like tests really aren't. For example, in a Newtonian system of identical particles that ... 6answers 15k views Newton's cradle Why, when one releases 2 balls in Newton's cradle, two balls on the opposite side bounce out at approximately the same speed as the 1st pair, rather than one ball at higher speed, or 3 balls at lower ... 3answers 4k views What's wrong with this derivation that$i\hbar = 0$? Let$\hat{x} = x$and$\hat{p} = -i \hbar \frac {\partial} {\partial x}$be the position and momentum operators, respectively, and$|\psi_p\rangle$be the eigenfunction of$\hat{p}$and therefore $$\... 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 ... 5answers 3k 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 ... 7answers 7k views The best way in which a man can pull a train I have chosen this example as a paradoxical limit, but my question really regards the optimization, distribution and outcome of force when you try to pull a weight: how can you optimize your effort/... 5answers 1k 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, ... 3answers 400 views Momentum of transverse waves on a string In general, if a wave carries energy density u with velocity v, it also carries momentum density u/v. I've seen this explicitly shown for electromagnetic waves and (longitudinal) sound waves. ... 1answer 1k views Do neutrinos refract? The most benign of interactions is refraction. While neutrinos rarely interact with matter in a sense like the photoelectric effect, does that mean that they don't refract either? 4answers 2k 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 ... 6answers 1k 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}}$$where \vec r_i ... 6answers 10k views What is canonical momentum? What does the canonical momentum \textbf{p}=m\textbf{v}+e\textbf{A} mean? Is it just momentum accounting for electromagnetic effects? 8answers 5k views Does leaning (banking) help cause turning on a bicycle? I think it's clear enough that if you turn your bicycle's steering wheel left, while moving, and you don't lean left, the bike will fall over (to the right) as you turn. I figure this is because the ... 3answers 2k views Center-of-mass frame for massless particles Given a scattering event where a photon and electron go in and a photon and electron come out, what is the center of mass frame? I'd say, since the photon has no mass, it's the rest frame of the ... 4answers 1k views Energy is actually the momentum in the direction of time? By comparatively examining the operators a student concludes that `Energy is actually the momentum in the direction of time.' Is this student right? Could he be wrong? 11answers 52k views How can momentum but not energy be conserved in an inelastic collision? In inelastic collisions, kinetic energy changes, so the velocities of the objects also change. So how is momentum conserved in inelastic collisions? 3answers 2k views What are some phenomena that can not be described without the help of Newton's third law of motion? [closed] What are some phenomena that can not be described without the help of Newton's third law of motion? All the phenomena I can think of can be explained with the help of Newton's first law or second law. ... 5answers 13k views How to get the position operator in the momentum representation from knowing the momentum operator in the position representation? I know that$$\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, ... 2answers 27k 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 ... 1answer 833 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 ... 8answers 7k 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 ... 4answers 3k 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 ? 10answers 3k views 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 ... 7answers 3k views Ball flying towards me or me flying towards ball Suppose a ball is flying towards me at a speed of 10m/s and that, on impact, I feel "x" amount of pain. If, instead, it was me flying towards the ball at the same speed, with all other conditions ... 2answers 8k 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 ... 1answer 536 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 ... 4answers 58k 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 ... 4answers 36k 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 ... 6answers 10k 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? 1answer 4k 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 -i\... 4answers 4k 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 time/... 5answers 7k views Spontaneous pair production? So I've been looking into particle-antiparticle pair production from a gamma ray and don't understand one thing. Let's say I have a 1,1 MeV photon and it hits a nucleus - electron-positron pair with ... 3answers 1k views Trouble with the Lorentz law of force: Incompatibility with special relativity and momentum conservation? In Physical Review Letters, there was a paper recently published: Masud Mansuripur, Trouble with the Lorentz Law of Force: Incompatibility with Special Relativity and Momentum Conservation, Phys. ... 3answers 727 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? 4answers 4k 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 ... 4answers 463 views A question about E=pc for massless particles Since photon has no (rest)mass and$$E^2=(pc)^2+(mc^2)^2$$we derive that E=pc for particle with no (rest)mass. However, if we transform the non-relativistic formula for kinetic energy$$E_k=\... 4answers 15k 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 ... 2answers 653 views Momentum and spacetime My apologies up-front for the naive question and my rudimentary understanding, but I should be delighted if someone would enlighten me :) The question has to do with the application of the ... 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, $$... 5answers 2k views Elastic collision of point particle and rod A 1 meter long rod on the ice with mass m_2=1 kg is perpendicularly hit on one end by a point particle with mass m_1=0.1 kg. The collision is elastic and the point particle is bounced back in the ... 2answers 286 views Deriving the expectation of [\hat X,\hat H] For a free particle of mass m, with Hamiltonian$$\hat{H} = \frac {\hat{P}^2} {2m},$$where$$\hat{P} = -i \hbar \frac{\partial} {\partial x}.$$The commutative relation is given by$$[\hat{X}, \... 2answers 590 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 F_{...
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, work,...
$E = h\nu$ 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 ...