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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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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1answer
1k views

How do I show the fractional change in Kinetic Energy in a completely inelastic collision?

Given the formula $$\frac{{\Delta}(KE)}{KE_i}=\frac{(KE_f-KE_i)}{KE_i}=\frac{-M}{(m+M)}$$ Now I know these that the conservation of momentum is always applicable. Also I understand that ...
3
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1answer
99 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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506 views

Atmospheric pressure's effect on sound

An argument has been travelling in amongst my friends around this matter and after listening about it for 3 whole days I decided to ask it here. The Question is: Would a high atmospheric pressure ...
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175 views

Question relating to energy transfer in between two particles

How would I go about calculating the maximum kinetic energy transferred from one particle when it forms an elastic collision with another particle. For example, if I had two billiards one with mass m ...
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1answer
440 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 ...
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2answers
2k views

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

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 ...
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75 views

Four-momentum, four-velocity, energy

If given the four-momentum of any particle monitored by an observer as: p = $p^\hat{α}e_\hat{α}$ using unit vectors in observer’s reference frame and u = $e_\hat{0}$ then I get I'm just ...
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3answers
1k 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 ...
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1answer
117 views

Question on the negativity of the coefficient of restitution

I was trying to solve a Mechanics question on Momentum. Here is the question : Two small smooth spheres A and B have equal radii and have masses m and km respectively. They are moving in a ...
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1answer
370 views

What are the general solutions to a hard sphere collision?

Surely someone has found the solutions to the hard sphere collisions (in $n$ dimensions) of two bodies of mass $m_1$ and $m_2$, respectively--that is the resultant velocities (or momenta) of the two ...
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0answers
74 views

Momentum of capacitor in a uniform magnetic field

We are observing ideal, charged, parallel plate capacitor placed in uniform magnetic field parallel to plates. Whole system is at rest and isolated (we have forces that hold plates separated, but net ...
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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 ...
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3answers
4k views

When is momentum not conserved?

What are some common examples where momentum is not conserved? This question arose in my mind when I read that a ball dropped from a height penetrates into a bed of sand and that momentum is ...
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2answers
888 views

Punching - Force or Momentum?

If I want to punch a person inflicting maximum damage, what do I need to care about? My force of punching, i.e, do I need more acceleration? Or do I need momentum, i.e my velocity for punching?
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4answers
108 views

Can conservation of momentum and conservation of energy explain every possible event in the Universe?

I heard my friend, a researcher, say that we can, in theory, explain every event happening in the universe using the Conservation of momentum and energy. He added that we may not be able to do that ...
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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
55 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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1answer
219 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
77 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
100 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
92 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
186 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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102 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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187 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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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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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
994 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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195 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
126 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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132 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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375 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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201 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
525 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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9answers
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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
250 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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107 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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84 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
62 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
110 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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8answers
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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?
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1answer
48 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
105 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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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 ...
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1answer
85 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
60 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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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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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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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 ...