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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Momentum of electron problem [duplicate]

Recently, my friend bemused me with a question related to the momentum of an electron. The confusing logic is stated below: Since an electron is a particle and according to classical physics, we know ...
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2answers
132 views

Recommendation on ADM mass and Bondi mass

I want to learn some advanced topics in GR, such as ADM 4-momentum and Bondi 4-momentum. However nearly no textbooks on GR contain this area, such as Wald, MTW, Hawking, Carroll and Zee's. Can anyone ...
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340 views

Directional derivatives in the multivariable Taylor expansion of the translation operator

Let $T_\epsilon=e^{i \mathbf{\epsilon} P/ \hbar}$ an operator. Show that $T_\epsilon\Psi(\mathbf r)=\Psi(\mathbf r + \mathbf \epsilon)$. Where $P=-i\hbar \nabla$. Here's what I've gotten: ...
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1answer
126 views

Why do safety helmets have a softer inner layer nearer the head?

I know that when an object collides onto the helmet, it causes an inelastic collision so that energy is absorbed by the structure of the helmet, so what exactly does the softer inner layer do? Does it ...
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1answer
177 views

How similar is comparison between the principle behind Newton's Cradle versus AC Current moving down a transmission line?

Anyone who has taken high school physics has seen the following assembly. You drop one ball from the left hand side and the ball from the farthest right hand side gets knocked away. This is to ...
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2answers
139 views

Is the energy of momentum stored physically? [closed]

While an object is moving, relativity will say it weighs more, especially so as it approaches light speed. The increase in energy is then easily sensed as an increase in mass (Almost as a rock in ...
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2answers
245 views

Momentum vector transformation

I am confused about the way momentum vector transforms in the following case: $$q_k \to q_k'= q_k + \epsilon f_k(q)$$ The Jacobian is thus $\Lambda_{ij} = \frac{\partial q'_i}{\partial q_j} \approx ...
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1answer
189 views

Motivating the ansatz for the infinitesimal translation operator

I'm reading Sakurai's Modern QM right now and in the first chapter he states a number of conditions required for a translation operator: unitarity, ...
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2answers
803 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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3answers
127 views

Different results to a basic question ( Newton's law and perservation of momentum)

Trolley with mass of $m_0=1 \ kg$ is moving without friction on the railway track. It is raining so there is a constant mass flow of water $\Phi_m=0.1\ kg/s$. Constant force $F=0.1 \ N$ is ...
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1answer
4k views

What formula connects the moment of inertia and angular velocity? [duplicate]

I need to determine angular velocity of a disc when a man with given mass and speed whacks on the edge of it. I calculated the total moment of inertia of disc and body, how do I calculate the ...
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3answers
2k views

Conservation of linear and angular momentum

Suppose I have two rigid bodies A and B and they are connected by a spring which is attached off-center (thus possibly causing torques). Due to the spring a force $f$ acts on A and a force $-f$ acts ...
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4answers
466 views

Since everything with mass exerts a gravity force on everything else, why do objects float in outer space?

For example, if you were to go out into deep space, and just slow down and stop your rocket. Everything inside the rocket that's not strapped in, starts floating. Why is that if every object has mass ...
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2answers
208 views

What moves an object? Momentum or Kinetic Energy? [duplicate]

What exactly makes an object move? Momentum is $\vec p= mv$ where $m$ is mass of an object and $v$ is the velocity of an object, and as a result of this when I fire a bullet the bullet may travel much ...
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0answers
209 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 ...
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2answers
1k 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 ...
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1answer
408 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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5answers
1k views

Is the canonical momentum conserved when a particle moves in magnetic field?

Here is a question about the canonical momentum that I had asked some days ago, but I still have one point that I am not understand. Considering a particle moves in a magnetic field with charge $q$ ...
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8answers
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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 ...
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2answers
450 views

Photons have no mass. So, why does $E = pc$ hold? [duplicate]

It's a somewhat theoretical question. In special relativity, The energy of a photon is given by $E = pc$. But, my argument is that, since photons have no mass, how can they have a momentum $p$? The ...
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3answers
115 views

Integral ambiguity

I'm a bit confused with some notation I encounter in physics calculus. Consider this: Taken from here. Integration operates on functions, correct? What does it mean to integrate $\frac{d{\bf ...
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0answers
108 views

Poynting Vector Volume Integral Inside a Cavity

Given an electromagnetic wave in resonance mode in a vacuum cavity inside a perfect conductor, on the boundary, the parallel component of $E$ field vanishes, and the perpendicular of component of $B$ ...
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1answer
66 views

$\dot \omega $ when momentum is conserved

If momentum is conserved when there is no externel force, why is there an acceleration when a momentum parameter is changed (inertia)? How does it accelerate with no external force? For example ...
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1answer
188 views

Simple expression for transitional pressure force

Consider a simple, circular orifice with an upstream, high gas pressure and downstream, normal atmospheric pressure. Consider also a flat circular plate that can be positioned anywhere along the ...
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1answer
53 views

Sub-light speeds and momentum conservation law

Let's imagine a boat on a lake. Observer A is sitting on the shore. Observer B is sitting in the boat on the bow. Observer B has a ball attached to the end of a string which he holds in his hand. ...
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1answer
124 views

When I move my arm forward in vacuum, will my body move backward?

Let's say I stay at point $x=0$ in vacuum. When I move my arm forward such that it will have a positive $x$ position (say $x=5$) will the rest of my body move backward such that it will have a ...
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1answer
172 views

Redshift of a reflected photon from a solar sail

Can someone help me understand my mistake here? I'm thinking of a photon travelling with momentum $p=h/\lambda$ which reflects off a solar sail of mass $m$ travelling with momentum $p_0$ in the same ...
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2answers
69 views

Flywheels and work

I'll start with a scenario for some control in the concepts I'm asking about today. Forgive me in advance, I never had the chance to explore physics in school, but I'd be happy to learn something new ...
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1answer
144 views

I need to know how many pounds of force a 3 million pound object has moving at 1 mph [closed]

How many pounds of force does a 3 million pound object have moving at 0.1, 0.5, and 1 mph?
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4answers
870 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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1answer
267 views

Conservation of energy and momentum via the continuity equation in asymmetric time and space translation

I am confused about energy and momentum conservation, time and space translation symmetry, and the continuity equation. Suppose we have a mass $m$ in inertial space far from any gravitational ...
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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 ...
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1answer
220 views

What force counteracts friction when a block is pulled?

Firstly, I understand and apologize that this is more of a physics question than a math question. I noticed that when I pulled a book out from under a pack of gum, the gum stayed largely in place (it ...
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2answers
75 views

Ziolkowsky Rocket Equation

I've looked at multiple sources on the internet and just can't wrap my mind around it. If I reference the wikipedia page on it; http://en.wikipedia.org/wiki/Tsiolkovsky_rocket_equation I am getting ...
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4answers
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How to calculate a collision which is partly elastic and partly inelastic?

(For the purpose of this question, "calculating a collision" means: given the velocities and masses of two objects in a collision, figuring out the new velocities of both objects after the collision). ...
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1answer
372 views

Heisenberg Uncertainty Principle

Question: The uncertainty in position is equal to the uncertainty in momentum. What is the uncertainty in velocity? What I did: I know that the uncertainty in position multiplied by uncertainty in ...
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6answers
15k views

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 ...
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3answers
132 views

Kinetic energy relationships with momentum and mass [closed]

If I have some arbitrary particle, we will call particle 1 and another particle 2 that have the same momentum, yet particle 1 has half the mass of particle 2, how does the kinetic energy compare ...
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2answers
2k views

Why is scattering vector $\vec{q}$ called vector of 'momentum transfer'?

In the world of scattering the angle at which you detect the scattered radiation is known as $q$, where $$ \vec{q} = \frac{4\pi\eta}{\lambda}\sin(\theta/2) $$ I read in a lot of books that this is ...
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2answers
140 views

Energy definition in special relativity

I'm going through the early homework assignments for my special relativity course and I've got myself a little confused about energy. I've got a basic understanding of what the 4-momentum is, having ...
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1answer
455 views

What factors indicates inelastic collision?

I am watching this example from Wikipedia: I am wondering what factors would indicate that the collision of 2 objects will be inelastic (I know macroscopic scale impacts are never perfectly ...
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1answer
44 views

Velocity change of objects

Is it possible for small object (small mass, let's say bullet) to hit large object (big mass, let's say rock) and still move forward (or stop) instead of being reflected (let's say objects don't crush ...
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2answers
52 views

How to cancel momentum without causing damage?

This is a fictional scenario I've designed and I'm trying to obtain a plausible logic for it to be somehow possible: I have a moving object, like a car or a person running, how can I stop it ...
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2answers
719 views

Calculating velocity change after impact?

Let's say there is no gravity here and objects won't crush. We have 2 rocks with $m=10\text{ kg}$. First rock has velocity $v_1=0\text{ m/s}$ and second $v_2=10\text{ m/s}$ (flying in leftward ...
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4answers
4k 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 ...
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2answers
124 views

Ballistic Pendulum Demo Problem

I have a question about the following problem: I got the solution $v=\frac{M+m}{m} \sqrt{2gh}$. But my real question is in the following picture: In the above slide, how can you derive ...
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2answers
105 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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159 views

Determine $p_x$ from $[x,p_x]=i\hbar $ [closed]

With $[x,p_x]=i\hbar $, how to determine the form of the operator $p_x$?
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3answers
392 views

Why does my gravity simulation do this? [closed]

For a school project i created a simple 2D gravity sim in Matlab using the simplest possible method. There are 2 nested loops so that the total force and acceleration of every object can be ...
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1answer
292 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 ...