In Newtonian mechanics, linear momentum, translational momentum, or simply momentum (pl. momenta) is the product of the mass and velocity of an object. It is a vector quantity, possessing a magnitude and a direction. If m is an object's mass and v is its velocity (also a vector quantity), then the object's momentum is
p
=
m
v
.
{\displaystyle \mathbf {p} =m\mathbf {v} .}
In SI units, momentum is measured in kilogram meters per second (kg⋅m/s).
Newton's second law of motion states that the rate of change of a body's momentum is equal to the net force acting on it. Momentum depends on the frame of reference, but in any inertial frame it is a conserved quantity, meaning that if a closed system is not affected by external forces, its total linear momentum does not change. Momentum is also conserved in special relativity (with a modified formula) and, in a modified form, in electrodynamics, quantum mechanics, quantum field theory, and general relativity. It is an expression of one of the fundamental symmetries of space and time: translational symmetry.
Advanced formulations of classical mechanics, Lagrangian and Hamiltonian mechanics, allow one to choose coordinate systems that incorporate symmetries and constraints. In these systems the conserved quantity is generalized momentum, and in general this is different from the kinetic momentum defined above. The concept of generalized momentum is carried over into quantum mechanics, where it becomes an operator on a wave function. The momentum and position operators are related by the Heisenberg uncertainty principle.
In continuous systems such as electromagnetic fields, fluid dynamics and deformable bodies, a momentum density can be defined, and a continuum version of the conservation of momentum leads to equations such as the Navier–Stokes equations for fluids or the Cauchy momentum equation for deformable solids or fluids.
Hello guys,
could someone give me a small hint to get me started on attempting this problem? I really cannot figure out how to relate conservation of momentum to the fact that there shouldn't be friction... does it have something to do with the so-called "sweet spot" of the ball?
But then...
Considering an atom within a rigid body, does the angular momentum of an electron within the atom vary when the body is put in motion?
My intuition is that, whether considered in a classical sense or quantum sense, the speed of a given electron in its motion within an atom will be constant and...
Question 2a: It is really hard for me to get my head around this.
The solution of this question mentions the momentum of the ball after it rebounds is 12kgms. My attempt at this solution is as follows
Before collision
Momentum of ball= mv= 2x3= 6 kgms and momentum of wall= 0
Therefore Total...
1 = elephant
2 = fly
So I am trying to find v'2 which is the final velocity of the fly. I have v1 the initial velocity of the elephant 2.1m/s. So I plug it into the equation and have v'2=(2m1/(m1+m2))*2.1m/s. We are not given the masses so I just know m1>m2 but I don't understand how that will...
If you put a hydrogen atom in a box (##\psi=0## on the walls of the box), spherical symmetry will be broken so ##n##,##l##,##m_l## are no longer guaranteed to be good quantum numbers. In general, the new solutions will be a linear combination of all the ##|n,l,m_l\rangle## states. I know that...
Hi all,
I'm opening this thread because of my uncertainty in how to correctly approach this exercise.
My first thought was that, since the plate is subject to friction with the floor, it is going to stop, thus the final moment is 0. Hence, from the conservation of linear moment:
$$m_Av_A+\sum...
In a closed system consisting of a set of particles not at rest relative to each other and acting on each other only by classical mechanical collision (i.e. billiard balls model, not including gravity or other long-range interactions), does conservation of momentum imply that the system will...
for the first question, i thougth that 0,5 A is the answer?
for the second question:
i used the E =hc/λ to found the E. but i got a little confused which equations to find ∆E, since there's no ∆t. or should i search the momentum, then use the λ= h/p ?
I got curious about firearm ballistics and googled something similar to "bullet momentum vs kinetic energy".
IIRC, momentum P = mv (checked); and kE = (mv^2)/2 (also checked).
So I essentially wondered if it's worse to get hit by a bullet with greater kE than by one with lesser kE, presuming...
A) and b) should be useful for solving the initial question.
If the truck is at rest initially, the magnitude of the momentum of the ball becomes ##|mv'|=|MV' - mv|##, but this may or may not be less than the magnitude ##mv##, depending on how large ##V'## is. ##V' = \frac{m(v+v')}{M}## in this...
The correct answer is:
#P = \int \frac{dp^3}{(2\pi)^3}\frac{1}{2E_{\vec{p}} \big(a a^{\dagger} + a^{\dagger}a\big)#
But I get terms which are proportional to ##aa## and ##a^{\dagger}a^{\dagger}##
I hereunder display the procedure I followed:
First:
##\phi = \int...
https://www.physicsforums.com/threa...f-a-translating-and-rotating-pancake.1005990/
So,I think I posted this in the wrong place. So, I will move it to here.
Here, in post #6, it is stated that ##\int R dm = M R##. As far as I know, R change from time to time and it is not constant. Hence, isn't...
So I have a trolley of mass m that moves on a straight line.
A sphere of mass m, is attached on the trolley with a light string of length a and it is left to oscillate.
Just to give some idea of their positions:
r_trolley = xi
r_sphere = (x-asinθ)i - acosθj (θ is the angle between the string...
I have read that the Schrodinger equation has no formal derivation we are simply applying the Hamiltonian operator on the wave function
$$\hat H = i\hbar \frac{\partial}{\partial t} = \hat T + \hat V$$
here we substitute $$\hat T = \frac{\hat p^2}{2m}$$ where $$\hat p = -i \hbar...
I am currently reading David Morin book and found this statement :
##\,\,\,\,\,\,\,\,## "It is important to remember that you are free to choose your origin from the legal possibilities of fixed points or the CM"
Is it really alright to choose the center of a...
In a head-on collision between the proton and electron, what is the squared 4-momentum transfer between the two particles.
Starting with the difference in momentum of the electron with the 4-vectors before and after the event: $$(P-P')^2=P^2+P'^2-2P\cdot P'$$
The circumstances are such that the...
Now, deriving relativistic momentum isn't terribly difficult, but that's not the same as understanding it. I'm trying to figure out why conservation of momentum in special relativity requires the gamma factor.
When I looked at conservation of momentum in elementary physics, we basically just...
I was thinking a little about how the absorption of angular momentum occurs from the point of view of QM. For example, suppose we have an atom A and an electron $e^-$.
The electron $e^-$ is ejected from a source radially in direction of the center of the atom. Suppose that the atom has net...
Help me understand a concept I came across by accident. So there is an axis (red) that is rotating with two rods attached to it (45 degrees from axis and 90 degrees with respect to one another) now if the balls at first are located closest to the red axis , as the axis begins to rotate the balls...
##\vec{L} = \vec{P} \times\vec{r}##
##L = mvr sin \phi##, where P = mv
Since ##\vec{r}## and ##\vec{v}## are always perpendicular, ##\phi## = 90.
Then, ##L = mvr##
At this point, I don't see how to get ##L = mvr = mr^2\omega##, using ##\omega = \dot{\phi}##
I know that ##\omega =...
While physics is generally believed to be CPT symmetric, there are processes for which such symmetry is being questioned - especially the measurement.
One of examples of (allegedly?) going out of QM unitary evolution is atom deexcitation - we can save its reversibility by remembering about...
I have read Classical Mechanics book by David Morin, and there are some parts that I do not understand from its derivation.
Note :
## V## and ##v## is respectively the velocity of CM and a particle of the body relative to the fixed origin , while ##v'## is velocity of the particle relative to...
Hi all!
These days I am brushing up my knowledge on EM Waves. I begin with the introductory level but I don't mind to engage in an advanced treatment of the topic.
At the very basic level I had a high school book, the mentions straightway that if the wave carries with it an energy U, it posses...
If you were to fire a single atom from a fixed point into a chamber of perfect vacuum and measure where it collides with the opposite wall. Could Spontaneous symmetry breaking in the sub atomic particles cause momentum change in the atom, changing the part of the wall the atom interacted with?
So we all know that the form of the momentum operator is: iħd/dx. And for energy it is iħd/dt. But how do we derive these operators?
The only derivations of the i have seen is where the schrødinger equation was used, but that makes the logic circular, because the Schrødinger-Equation is derived...
The goal I am trying to achieve is to determine the momentum (2D) in a quantum system from the wavefunction values and the eigenergies. How would I go about this in a general manner? Any pointers to resources would be helpfull.
I am trying to find the equations of motion of the angular momentum ##\boldsymbol L## for a system consisting of a particle of mass ##m## and magnetic moment ##\boldsymbol{\mu} \equiv \gamma \boldsymbol{L}## in a magnetic field ##\boldsymbol B##. The Hamiltonian of the system is therefore...
Hello! I found this formula in several places for the total angular momentum of a particle with intrinsic spin 1/2 and angular momentum l=1 in the non-relativistic limit:
$$\frac{1}{\sqrt{4 \pi}}(-\sigma r /r )\chi$$
where ##\sigma## are the Pauli matrices and ##\chi## is the spinor. Can someone...
Consider a car slamming into an unyielding wall at 60 mph. Objects in the car will be slammed against the dashboard with a certain amount of force.
Now, instead of slamming into a stationary wall, you slam into another car coming towards you at 60 mph. Relative speed, 120MPH.
QUESTION: Will...
I've been noodling around with derivations of the relativistic energy and momentum, and I almost got it down to just a few lines. But not quite.
I'm going to work in one spatial dimension, for simplicity (even though some derivations require a second spatial dimension)
Let's assume that there...
Since it asks for the time evolution of the wavefunction in the momentum space, I write : ##\tilde{\Psi}(k,t) = < p|U(t,t_{0})|\Psi> = < U^\dagger(t,t_{0})p|\Psi>##
Since ##U(t,t_{0})^\dagger = e^{\frac{i}{\hbar}\frac{\hat{p^2}t}{2m}}##, the above equation becomes
##\tilde{\Psi}(k,t) =...
I made a new version of the falling cat video, with narration. It explains how cats turn around while having zero net angular momentum during the fall:
I've a body having initial angular velocity at ## t=0 ## as shown. The axis shown are fixed in inertial space and initially match with the principal axis. I want to find the infinitesimal change at ##t+\Delta t## in the angular momentum along the ##z## axis.
I've seen the following approach...
The given lagrangian doesn't seem to correspond to any of the basic systems (like simple/ coupled harmonic oscillators, etc). So I calculated the momentum ##p## which is the partial derivative of ##L## with respect to generalized velocity ##\dot{q}##. Doing so I obtain
$$p =...
A disc initially has angular velocities as shown
It's angular momentum along the y-axis initially is ##L_s##
I tried to find its angular momentum and ended up with this:##L=I_{x} \omega_{x}+I_{y} w_{y}+I_{z} z_{z}##The z component of angular momentum is thus ##L_{z}=I_{z} \omega_{z}##
However...
Ball X has mass 0.03kg. It falls vertically from rest from a window that is 30 m above the ground. Ball Y has mass 0.01kg. At the same time that Ball X starts to fall, Ball Y is projected vertically upwards from ground level directly towards Ball X. The initial speed of Ball Y is 20 m/s...
Answer is (a)
I thought it would be (b) due to conservation of momentum - so final momentum of the hockey stick is equal to the initial momentum of the ball. I assume this isn't correct because there are other external forces acting (air resistance?) Is that sound?
A hockey ball of mass 0.2kg is hit so that its initial speed is 8 m/s. The ball travels in a horizontal straight line with acceleration given by a= - 0.5- kt where t is the time in seconds measured from when the ball was hit. After 2s the ball has traveled 41/3 m. It is then intercepted by a...
It's been a few years since I failed my physics degree but I still really want to reach an understanding of QM, and I'm currently going through a QM textbook.
One thing I cannot understand no matter how much I think about it, is momentum uncertainty. In classical mechanics a specific kinetic...
My understanding is that virtual particles don't really exist. However, they somehow come into existence under certain circumstances. For example, in the Casimir Effect the virtual particles on the outside of the plate now have the capacity to transfer momentum and kinetic energy to the...
I aready got the solution for this exercise. However, the solution used the referance frame from the car:
What I'm trying to understand is the line:
Because before reading the solution, I was trying to solve it using the lab frame.
So this is my work so far:
Using conservation of momentum and...
Good night. I have a doubt, what is the meaning of the coherent states superposition of momentum?
In a many of places, sites I see an explanation for the equations but I never see the explanation between diffences of the superposition of position from momentum.
Hi everyone,
In my physics class, we are doing the Hollywood Physics Project. It's a project where you analyze the physics from a scene in a movie and talk about if it's accurate or not. I chose the scene from the Avengers where Thor strikes Captain America's shield with his hammer. The...