# 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.

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### Where does $\hat{P}\psi(x) = -i\hbar \partial_x \psi(x)$ come from?

It's a very basic question, where does the relation $$\hat{P}\psi(x) = -i\hbar \partial_x \psi(x)$$ for any square integrable $\psi(x)$ come into existence? Some texts I found states that the above ...
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### 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. ...
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### what is actually mean by momentum in deepest level of physics?

What does something called "Momentum" actually measure?I know that generally momentum of a object is describe by the multiplication of mass and object's velocity and it is a conserve quantity without ...
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### Can deformations of time-space continuum violates law of momentum conservation?

Based on Einstein’s theory of relativity a mass as property of physical objects creates deformation of time-space continuum. Therefore the light path bends in gravitational fields of massive objects. ...
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### Does momentum scale linearly with time, assuming a constant nonzero net force, even at relativistic speeds?

I would expect it to, since you'd think the loss of velocity due to relativity would be made up for by the gain in relativistic mass. I'd like this to be confirmed, though. and if so, in whose ...
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### How do you determine which way two objects will travel after collision when given their respective masses and speeds?

I was practicing some Mechanics, and I came across a problem that involved an impact between two objects: I understand how to approach the question: Apply the conservation of momentum, and use the ...
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### Conservation of momentum when one body is fixed

When we fire a gun, it recoils. Both bullet and gun gain in momentum. Before the shot, momentum of both is zero. If we make the gun unmovable somehow, after the shot, what will be the effect on the ...
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### When a bomb explodes, does it momentum remain same?

If, from an aircraft, a bomb is thrown to an object placed at ground and bomb explodes before it hits the object, i.e if it explodes in the middle of its path, does it momentum remain same? I knew ...
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### Why don't two objects move with the same velocity after collision?

I have a problem with understanding the nature of collisions and their outcomes. From my understanding, I come to think that when a mass collides with another, both of them should always have equal ...
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### Are asymptotic states in scattering experiments really momentum eigenstates?

In a typical collider experiment, two particles, generally in approximate momentum eigenstates at $t=-\infty$, are collided with each other and we measure the probability of finding particular ...
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### Zeroth component of 4-momentum and relativistic energy-momentum relation

As I understand it one is forced to use 4-vectors since we require objects that transform as vectors under application of Lorentz transformations and 3-vectors do not (technically they do under ...
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### Momentum conservation problem, elastic collision [duplicate]

This question has got me thinking for a while now and I haven't been able to come up with any answer at all. I've done the basic conservation of momentum, kinetic energy but I have no idea how to ...
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### Variation of Veritasium bullet block experiment

I'm new here. this is in reference to the video posted by veritasium on the bullet block experiment. i realise there is already a thread on this but i want to ask a variation of the question. so ...
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### How to calculate impulse required to move an object vertically upward by given distance [closed]

Suppose I have a stationary object of mass $m$ and I want to apply a momentary force in the vertical direction so that it just reaches the height $h$. So how do I calculate the impulse required in ...
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### Momentum of a rack and pinion gear system excited by a time variant force

Background I have a rack and pinion gear system as shown in the image below The pinion gear is attached to a flywheel at the back. The first state of the system, none of the gears or the ...
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### Relating Initial velocity and acceleration to distance traveled up a ramp

This is the situation: I am conducting research on the ability of fin-fish to scale short wetted ramps for use alongside sea-lamprey barriers to allow non-target species to pass these barriers. We ...
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### Why is the acceleration of the center of mass is equal to 0 in this problem?

I don't understand why the center of mass' acceleration is equal to 0 when the center of mass should be moving as an external force is exerted on the cue ? Billiard Balls. Now we can go back and ...
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### Is the eigenvalue of Hamiltonian invariant under linear transformation of momentum operator?

It is given The dynamics of a particle moving one-dimensionally in a potential V(x) is governed by the Hamiltonian $H_0 = p^2 /2m + V(x)$, where $p = -i\hbar d/dx$ is the momentum operator. ...
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### Question about Thrust; am I correct?

Basically, here's what I understand about Thrust: Thrust is a force. You get it by doing $v\times\frac{dM}{dT}$. Pretty basic, because that's the formula you're given. However, because I'm trying to ...
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### The ratio of masses in an elastic collision [closed]

Two blocks of mass $M_1$ and $M_2$ moving along a 1-dimensional straight line with velocities $V_1$ and $V_2$, respectively, collide elastically. After the collision they move with respective ...
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### When to consider friction as an impulsive force?

Suppose a ball obliquely strikes a rough horizontal surface then it experiences a frictional impulse and conservation of linear momentum cannot be done on the horizontal direction. Now consider ...
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### What is the minimal G-force curve in 2-dimensional space?

Given two parallel roads, which need to be connected, what shape of curve would produce the minimum overall horizontal G-force(s) on travelers? Is it a $sin$ or $cos$ wave? Is it a basic cubic ...
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### Is it possible to measure the spin of an electron without moving it?

I know that the position and spin operators commute, so it is theoretically possible. What I want to know is, what experiments currently exist that achieve this?
Here are the proofs regarding the center of mass motion as reported on my book. $$\vec{r_{cm}}=\frac{\sum\vec{r_i} m_i}{\sum m_i}$$ $$\vec{v_{cm}}=\frac{d{\vec{r_{cm}}}}{dt}=\frac{1}{M}\sum \frac{d}{... 1answer 19 views ### Spheres collide with merry-go-round [closed] Four spheres, with uniform densities \rho_1, \rho_2, \rho_3, \rho_4 and radii r_1, r_2, r_3, r_4, respectively, roll without slipping with constant velocities v_1, v_2, v_3, v_4 along tracks ... 3answers 112 views ### Same quantum states represented in different basis In literature on an introduction to quantum mechanics which I am working through, there is a section which explains that a vector has different representations based on the basis you choose and then ... 2answers 348 views ### Schrödinger equation in momentum space In literature on an introduction to quantum mechanics which I am working through, there is a section which explains that a vector has different representations based on the basis you choose. It then ... 1answer 47 views ### Is Momentum conserved in this block-wedge system? There's a block slides downward along a frictionless wedge which sits on a frictionless horizontal surface, when the block leaves the wedge, both of the wedge and the block have a horizontal velocity ... 2answers 67 views ### Does inelastic collision say the ball bounces back to you when thrown at an angle on ground? I created a bounce simulation using exactly the formula from Wikipedia. The behavior I observe is not what I would expect in two cases: When two balls hit off-centre, they act the same as if the ... 0answers 53 views ### Heisenberg theory of uncertainty I was watching a video on YouTube about uncertainty theory of Heisenberg it said that there is a relation between momentum (multiple of mass and speed) and wave length. And the relation is that if ... 1answer 23 views ### A person on a concrete slab on a frozen lake starts walking  2 m/s, what is the speed of the concrete slab? [closed] Full question: My attempt: Let the M be the mass of the person. Let x be the length of the slab. The original center of mass is \frac{5M\frac{x}{2}}{M + 5M}. Let's say the person walks a ... 4answers 45 views ### Why are some system defined with the name “variable mass”? I do not get why system such as the rocket in space are defined as "variable mass" since the mass of the system is not varying. The equation used for such systems$$\sum F^{(E)}=\frac{d\vec{P}}{dt} \...
Consider the motion of a rocket of mass $m$ in space with gas expelled at relative velocity $u$. I found two different version of writing the momentum of the system on Klepper Kolenkow and Morin book. ...