Questions tagged [momentum]

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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31 views

Doesn't universe violates law of conservation of linear momentum?

As mass of universe is not constant,it means that its linear momentum is not constant.But thinking in another way,is universe subjected to a net external force?But what is external for universe?...
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Does linear momentum of a hydrogen atom-system remain constant during electronic transitions?

When electronic transitions(excited to ground) take place in a hydrogen atom, does the linear momentum of proton-electron system remain constant?
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Proof that the momentum operator is hermitian without assuming the wavefunction approaches zero at infinity?

I am currently taking my second semester of quantum mechanics. For a number of proofs in the course, we have used the assumption that the wavefunction goes to zero at infinity. We have simply used the ...
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Proof that $v=\frac{dE}{dp}$ at relativistic speeds?

This is a formula I have seen stated in two different places in a relativistic context, but I do not know the proof and seem unable to derive it on my own. $E$ is the energy of a free particle, $v$ is ...
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A ball of mass $m$ is dropped from a height $h$ on to a rigid floor. If $e$ is the coefficient of restitution [on hold]

A ball of mass 'm' is dropped from a height 'h' on to a rigid floor. If e is the coefficient of restitution, the time required for the complete bounce is? After finding the initial and final velocity ...
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How to find the acceleration of two blocks? [on hold]

Help I'm really lost. I'm not even sure what forumla im supposed to be using on this problem A 15 kg block is placed on top of a 25 kg block (see figure below). A force of 387 N is applied to the ...
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Is the coefficient of restitution always equal to the square root of the ratio of final kinetic energy to the initial kinetic energy?

The coefficient of restitution (COR) according to some sources (https://en.wikipedia.org/wiki/Coefficient_of_restitution) is equal to the square root of the ratio of final kinetic energy to the ...
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Why is the momentum always conserved in elastic collision?

As the title above, why is the momentum always conserved in elastic collision (no loss of kinetic energy)? Does it related to the conservation of kinetic energy? If so, how do we prove that? Further ...
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How do we calculate the force applied by a ball on a wall which bounces back? [on hold]

If we have a ball which we throw toward a wall which touches the wall and bounces back then how will you calculate the force applied by the wall on the ball because the the contact time of the ball ...
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Is it Valid to Derive $E = pc$ From the Energy-Momentum Relationship for Photons?

Given a particle with mass $m$ moving at velocity $v$, total energy is: $$E^2 = (pc)^2 + (mc^2)^2$$ Note I am not using the relativistic - rest mass convention, as I was taught to think in ...
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Newton's Third Law of Motion? [duplicate]

Newton's third law of motion states that every action has an equal and opposite reaction. But, on punching a wall, I feel much greater force than on punching an inflated balloon. So, what does it mean?...
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Sign of stress tensor in momentum conservation equation

I have a confusion and would be grateful if anybody could help clear it up. So I was reading Kip Thorne's modern classical physics and came up on the following definition of stress tensor: $T_{ij} $ ...
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The force exerted by a single molecule

In the chapter of the kinetic theory of gases in a basics undergraduate physics book, it says the force exerted by a single molecule on a wall is calculated as $F = \frac{\Delta p}{\Delta t} = \frac{...
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What is the reason that conservation of momentum is conserved in nuclear reactions?

I understand that in nuclear reactions such as fusion or fission, it is known that energy released due to the mass defect to obey the conservation of energy. However, researching online; I fount ...
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Conservation of angular momentum and its prediction by Newtonian Physics

The situation, in brief, is that newtonian physics is incapable of predicting conservation of angular momentum, but no isolated system has yet been encountered experimentally for ...
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Collisions in a System of Bodies

There are three blocks A,B and C, with B and C at rest connected by a light spring and A moving with a velocity v, all three lying on the same horizontal frictionless surface. After some time A ...
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Why is tangential particle momentum conserved in a collision?

In my dynamics class, we learned that the individual momenta of two colliding particles is conserved in the direction tangential to the collision. Why would this be the case? Consider the diagram ...
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Derive canonical momentum in electromagnetic field without knowledge of Lagrangian and Hamiltonian mechanics

One of my friend is studying quantum mechanics and he asks me a lot. This time, he asked me about the momentum expression in Hamiltonian of charged particle in electromagnetic field. $$H = \frac{1}{...
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How does $p\cdot u$ relate to observed energy and momentum for a massive particle?

Gravitation by Charles W. Misner, Kip Throne and John Wheeler page 65 Exercise 2.5. The book defined "energy" for a photon $E=-\mathbf p\cdot \mathbf u$ for subsection 2.8, which later explained as a ...
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de Broglie equation has momentum=$mv$ not $mc$. why? [closed]

de Broglie equation that is $$\lambda=\frac{h}{mv}$$ This equation is derived from $E=mc^2$, so why is momentum taken as $mv$ and not $mc$? Because $E=mc^2$, not mv^2
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How does specifying a vacuum-state fix the field-momentum-operator for given CCRs?

This is kind of a follow-up question to my last question about the uniqueness of the field-momentum-operator. The answer stated that the commutation-relation alone does not fix the field-momentum ...
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Force applied to a variable section pipe

In the case of an ideal, incompressible and steady flow of an ideal fluid of density $\mu$ through a linear pipe with a variable section, assuming a unidimensional flow, I have been given that the ...
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Reducing the degrees of freedom of a Lagrangian in a spherical potential by using integrals of motion [duplicate]

I'm sure I've made a silly mistake here, so I would be very grateful if someone could help me clear it up! Here is my reasoning: The Lagrangian in a spherical potential is $$ \mathcal{L}=\frac{m\...
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Magnetic Vector Potential - a measure of Momentum

I am trying to understand the magnetic vector potential as momentum per unit charge, that is, somehow, the "total" momentum should be $p = mv +qA$. Here's a part of the paper I was reading - I am ...
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What is the total momentum of EM fields?

I have an assignment where i have to find the total momentum of an EM field. Imagine a perfect magnetic dipole in (0,0,0) with dipole moment $$ \mathbf{m} = m\mathbf{\hat{z}} $$ And also a point ...
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Where is the momentum going?

When a ball of mass $m$ collides elastically having velocity $v$ with a wall, then it retraces itself with the same velocity. Impulse on the ball due to wall is $2mv$ and since there is no external ...
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Rolling ball while winding a tape [closed]

I've been trying to solve this for a hours but i can't build the equations related problem involving this question, could someone help me? a ball of mass $m$ and radius $r$ rolls down without sliding ...
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Generator of spatial translation in field theory

In classical mechanics, we know that the momentum operator is the generator of spatial translation. But it seems to me that this is no longer the case in the classical field theory. Lets first ...
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Energy loss in sticky collisions

A typical problem of sticky collisions involves an object colliding with an object at rest on frictionless surface, and the two move together. If conservation of momentum is applied we get $ v'=\frac{...
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Discussion regarding work done? [closed]

Suppose I take a box with some masses and pull it along the table at a constant speed. In this case, there is a force pulling to the right (the string) and a frictional force pulling to the left. ...
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Is the field-momentum operator ambiguous?

In this question I asked wether the definition of the momentum operator as an operator that has to generate translations by satisfying the canonical commutation relations was ambiguous. The answer to ...
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Momentum in complex scalar field

Consider a complex scalar field $\psi(x)$ with Lagrangian density $$ \mathcal{L} = \partial_\mu\psi^* \partial^\mu\psi - M^2\psi^*\psi. $$ Expand the complex field operator as a sum $$ \psi = \int \...
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How can i find the velocities after the collision on this oblique collision problem [closed]

I found this excercise in my textbook but i couldnt finish it. Object $A$ with mass $m_1=m$ and velicity $u=12 m/s$ collides with object $B$ with mass $m_2=2m$ and velocity $u'=0$. After the ...
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Why the energy and momentum conservation equations do not include terms reflecting the particle nature of the photons? [closed]

It is well known that light has a dual nature. However, the energy and momentum conservation equations embody the wave aspect of light but not the material aspect of the photon. Should there be ...
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Linear momentum of a system remains conserved, but with respect to which frame of reference?

I have studied that linear momentum of a system remains conserved. But i can't figure out with which reference of frame it is conserved. Is it conserved with respect to system reference frame or in a ...
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Hamiltonian operator in polar coordinates with momentum operators

The Hamiltonian operator for a free non-relativistic particle looks like $$ \hat{H} = \frac{\hat{p}^2}{2m} = -\frac{\hbar^2}{2m} \nabla^2. $$ In polar coordinates, the Laplacian expands to $$ \...
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The impulse on a wall

If a ball was thrown to a wall, How could we calculate the impulse on the wall ? For example, if I throw a $2kg$ ball with $ 4m/s$, and it returned with the same speed but in the opposite direction, ...
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Should a wavefunction in momentum space be normalisable?

Is this a condition that the wavefunction in momentum space should be normalizable? Like we said that a particle has to be between ${-\infty}$ to ${\infty}$. Will the same argument also work for ...
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Will the rods rotate about the hinge after collision?

The problem is like this: two blocks(considered to be point masses) of masses $m$ are simultaneously moving with uniform velocities $v_0$ towards the rods and they hit the edges of rod and stick to it(...
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How to show that translational invariance in $y$ of implies that it's an eigenstate of $p_y$?

Let us consider a particle on a plane with uniform magnetic field $B=B\hat{z}$, and hence with the Hamiltonian $H=\frac{1}{2m}(\vec{p}+e\vec{A})^2$. I am concerned with finding the energy eigenstates, ...
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Is the change in momentum of each object in a collision the same?

I have this question concerned with collisions In the solutions, they work out the change in momentum of the blue car, which comes to 0.048. I also calculated the change in momentum of the red car 0....
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A problem about proof of Noether's theorem in Nakahara's Geometry, Topology and Physics [duplicate]

Nakahara's Theorem 1.1 (only the first half of the proof is taken) Let $H(q_k,p_k)$ be a Hamiltonian which is invariant under an infinitesimal coordinate transformation $q_k \rightarrow q'_k=q_k+\...
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How did we know that relativistic momentum is conserved in the first place?

From what I understand, people historically did a lot of experiments (or just life experience) realizing that a fast moving object of small mass has the same quantity of "something" that a slow moving ...
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Conservation of linear momentum with mass defect

Suppose we have an insulating container, like a perfect black body, which absorbs all the radiation coming from a radioactive element placed in the center (or some equivalent process like matter ...
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Energy and momentum

Does a muon or an electron with the same energy have the higher momentum? According to $E^2=m^2+p^2$ if you increase the restmass, the momentum must decrease. But if we look at a nonrelativistic case:...
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Simple exercise about conservation of momentum [closed]

A block of wood of mass $M$ is dropped, with no initial speed, from a height $h$ with respect to the ground. When it is at altitude $\frac{h}{2}$ it is hit by a bullet of mass m that travels ...
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Why there is no a vector quantity in $P=\sqrt{2mK.E}$

Personally, If I saw this law I would say that momentum is a scalar quantity, because I know that (scalar quantity X scalar quantity = scalar quantity). Since momentum is a vector quantity, So why ...
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Relative velocity, momentum conservation

I am having difficulty in conserving momentum for objects moving with relative velocities. For example: A block of mass $m$ with a semicircular track of radius $r$ rests on a frictionless ...
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How is linear momentum conserved in case of a freely falling body?

When an object is experiencing free fall, it has a constant acceleration and hence an increasing velocity (neglecting friction). Thus its momentum is increasing. But according to law of conservation ...
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Why is the relation between coefficient of restitution and air pressure of a basketball logarithmic?

Perhaps this is due to the spherical shape of the ball but yea, i've conducted the experiment for school and i'm trying to work through justifying this but need assistance. edit: here's the data