In physics, angular momentum (rarely, moment of momentum or rotational momentum) is the rotational equivalent of linear momentum. It is an important quantity in physics because it is a conserved quantity—the total angular momentum of a closed system remains constant.
In three dimensions, the angular momentum for a point particle is a pseudovector r × p, the cross product of the particle's position vector r (relative to some origin) and its momentum vector; the latter is p = mv in Newtonian mechanics. Unlike momentum, angular momentum depends on where the origin is chosen, since the particle's position is measured from it.
Just as for angular velocity, there are two special types of angular momentum of an object: the spin angular momentum is the angular momentum about the object's centre of mass, while the orbital angular momentum is the angular momentum about a chosen center of rotation. The total angular momentum is the sum of the spin and orbital angular momenta. The orbital angular momentum vector of a point particle is always parallel and directly proportional to its orbital angular velocity vector ω, where the constant of proportionality depends on both the mass of the particle and its distance from origin. The spin angular momentum vector of a rigid body is proportional but not always parallel to the spin angular velocity vector Ω, making the constant of proportionality a second-rank tensor rather than a scalar.
Angular momentum is an extensive quantity; i.e. the total angular momentum of any composite system is the sum of the angular momenta of its constituent parts. For a continuous rigid body or a fluid the total angular momentum is the volume integral of angular momentum density (i.e. angular momentum per unit volume in the limit as volume shrinks to zero) over the entire body.
Torque can be defined as the rate of change of angular momentum, analogous to force. The net external torque on any system is always equal to the total torque on the system; in other words, the sum of all internal torques of any system is always 0 (this is the rotational analogue of Newton's Third Law). Therefore, for a closed system (where there is no net external torque), the total torque on the system must be 0, which means that the total angular momentum of the system is constant. The conservation of angular momentum helps explain many observed phenomena, for example the increase in rotational speed of a spinning figure skater as the skater's arms are contracted, the high rotational rates of neutron stars, the Coriolis effect, and the precession of gyroscopes. In general, conservation limits the possible motion of a system but does not uniquely determine it.
In quantum mechanics, angular momentum (like other quantities) is expressed as an operator, and its one-dimensional projections have quantized eigenvalues. Angular momentum is subject to the Heisenberg uncertainty principle, implying that at any time, only one projection (also called "component") can be measured with definite precision; the other two then remain uncertain. Because of this, the axis of rotation of a quantum particle is undefined. Quantum particles do possess a type of non-orbital angular momentum called "spin", but this angular momentum does not correspond to a spinning motion.
When given a small displacement ##x##, the equation for m is:
(i) N sin θ = m.a where N is the normal force acting on the ball and θ is angle of the ball with respect to vertical.
(ii) N cos θ = m.g
So:
$$\tan \theta = \frac a g$$
$$\frac x R = \frac{\omega^{2} x}{g} \rightarrow \omega = \sqrt...
Hello everyone, I have a doubt regarding the conservation of angular momentum.
When dealing with collisions between two objects, if the net external force is zero we know that the linear momentum is conserved; even when the system is not isolated, for instance because of gravity acting on the...
I thought the answer is B because the angular momentum in conserved in all 3 pictures.
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Suppose we have a rotating body like a bicycle wheel in space away from gravity. This body stops after a while due to friction between the wheel and wheel axles. Is not the conservation of angular momentum violated?
Hello to everyone, first of all shame on me I has to ask and can not figure out it by myself...
The problem is I am trying to code game where two homogenous discs with same mass and same diameter, no fricition due to gravitational forces, can collide.
I can figure out the speed and direction...
One of the component of angular momentum operator is ##\hat{L}_{x}=\hat{y} \hat{P}_{z}-\hat{z} \hat{P}_{y}##
I want it's position representation.
My attempt :
I'll find the representation of the first term ##\hat{y} \hat{P}_{z}##. The total representation is the sum of two terms.
The...
I'm studying orbital angular momentum in the quantum domain, and I've come up with the Robertson uncertainty relation for the components of orbital angular momentum. Therefore, I read that it is necessary to pay attention to the triviality problem, because in the case where the commutator is...
a) We use the definition of linear speed in terms of angular speed:
v = r*omega
omega_f = v/r = (1.25 m/s)/(0.025 m) = 50 rad/s
omega_0 = v/r = (1.25 m/s)/(0.025 m) = 21.55 rad/s
b) We use the definition of linear speed:
v = d/t
d = vt = (1.25m/s)(74 min)(60 s/1 min) = 5.55 km
c) We use the...
I am trying to build a simulation of a car engine and wheels for a game project.
My model is currently this:
Engine outputs a torque -> this spins up a flywheel over time (the physics step of 1/60s) -> the flywheel is coupled with the clutch and thus transmission -> the transmission multiplies...
I have a problem in understanding angular momentum equation (mrv), especially the part where radius is involved.
imagine an elastic collision occurred between sphere of mass (M) attached to a string forming a circle of radius (R) and moving with velocity (V) and another stationary sphere having...
In other words, is there a rotational orientation of each atom in a monatomic gas (and corresponding rotational speed conserving angular momentum) that affects collisions, or does a substance need to have at least 2 atom particles to have the orientation/rotational ability to have particle...
The classic way to go about this problem would be to use Kepler's laws and thus find the new time period of earth.
However I encountered this question in a test on rotational motion which deals with conservation of angular momentum.
The equation used here would be I1ω1= I2ω2
Replacing I with MR2...
I understand that angular velocity is technically not a vector so does that mean the cross product of the radius vector and the angular velocity vector, the tangential vector, is also not a vector?
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...
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...
Dynamics Rigid body Kinematics problem, looking for angular acceleration of link BD and ED. AB has constant angular velocity of 45 rad/s CCW. Could y'all verify any mistakes in my solution? Thanks!
My line of thinking is as follows:
\omega_{PQ} = \frac{v_{\perp}}{\ell} = \frac v\ell \frac{\sqrt3}{2}
Similarly for rod ##QR##
\omega_{QR} = \frac{v_{\perp}}{\ell} = \frac v\ell \frac{\sqrt3}{2}
Is my reasoning correct?
First case, descends with the wheel:
mgh = .5(I)(w^2) ———- GPE converted to wheel energy
w = .1095. ———- rotation result is .1095
Second case, allow to free fall and impulse:
mgh = .5(m)(v^2). ———- GPE converted to kinetic energy
v = 7.746 ———-...
for (a) ##T=\frac {2\pi}{\omega}##
$$\omega=\frac {2\pi}{T}$$
$$\frac{d \omega}{dt}=\frac {-2\pi}{T^2} \frac {dT}{dt} $$
$$\alpha=\frac {-2\pi}{(2.94*10^-15)^2} = 7.27*10^29 rad/s^2$$
for (b) I'm understand that it's infinity, because the period is increasing indefinitely, so it's slowing...
I(i)w(i)= I(f)w(f)
I(i)= 1.08 x 10-3 kg·m2
w(i)= 0.221 rad/s
I(f)= mr^2 + I(i) = (5 x 10^-3)(.138)^2 + (1.08 x 10^-3)
(1.08 x 10-3)(.221) = ((1.08 x 10^-3)+9.22 x 10^-5))w(f)
w(f) = (2.3868 x 10^-4)/(0.00117522)
w(f)= 0.203094 rad/s
This is my attempt; however, I cannot seem to get it...
I calculate the gravity force
F = mg = (-9806.6)*(5.26e-1) = -5158 (mm^2*kg)/s^2
I get the moment
M = F*r = (-3.5e5)*(-6.81e1) = 3.5e5 (mm^2 * kg) / s^2 Where r is the y coordinate distance from origin to centroid
J = (Ix'...
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 far I have:
The velocity of the belt will be the same for pully A and D, so we can calculate the angular velocity of pulley D:
## V_A = V_B ##
## \omega_A r_A = \omega_D r_D ##
## ((20*3)+40)(0.075) = \omega_D (0.025) ##
## \omega_D = 300 Rad/s ##
My next step was to determine the angular...
Hi everyone :)!
I resolve this problem with components method and trigonometry method.
My results with components method its okay, but i can´t obtain the correct VE velocity.
Im sure that the problem its in the angles, but i don't know how to fix it.
The correct answers:
-Angular velocity...
Hello, I am trying to solve a problem involving a mass with known moment of inertia about an axis with a lever arm at angle theta and length r with a non-constant spring force acting at the tip of the lever arm and fixed distance away from the axis of rotation.
I am wondering what the best...
Hi! everyone! ;)
I have a problem with the development of this problem.
I need to resolve it with 2 procedures: trigonometry and instant centers. My advance can be see in the next image:
The instant centers procediment its (1) up and trigonometry procediment its (2) down.
I know that the...
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...
Hello,
I am currently working on a computer program to move on object undergoing circular motion in a spiral of decreasing radius. I hope this is illustrated clearly below (forgive me but it is a sketch and thus not precise in scale):
The scenario is as follows:
1. The object starts angular...
There are n vertical identical parallel identical cilinders rotating around their length axes with the same angular velocity. The are somehow fixed wrt to Earth and brought together (on a rail?). After the contact there is no slipping and the cilinders are coupled to their neighbor cilinders. It...
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...
##\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...
Hello. I am not familiar with spherical trigonometry while I am reading a solution in a GR problem book. It reads,
I study spherical trigonometry on Wikipedia and some other sites, but I am still not sure how to calculate the angular excess.
First, is angular excess equivalent to spherical...
Hi!
I would like to know how I could define an equation for α with given the two lengths of the rods and angle theta (θ). I sketched the situation below, the problem arises when the rod Lab has pasts the 180 degrees.
Like to hear.
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...
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...
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...
Here's the problem setup, my student and I are stuck.
A disk is rotating at constant angular velocity ω, and we are watching a point on the rim, parameterized by the angular position θ, move. Because we are observing the motion from an inclination angle Ψ, we do not always observe the...
From a previous post about the Relationship between the angular and 3D power spectra , I have got a demonstration making the link between the Angular power spectrum ##C_{\ell}## and the 3D Matter power spectrum ##P(k)## :
1) For example, I have the following demonstration,
##
C_{\ell}\left(z...
I assumed the angular velocity of the center of mass of the two discs about z axis to be w1
note that angular velocity of center of mass of both discs and center of anyone disc about z axis is same, you can verify that if you want, me after verifying it will use it to decrease the length of the...
Hi,
I need to come up with a math model for a digital ignition system. I've been thinking about it and I think that I need to measure 2 things to be able to calculate when I have to start charging the coil. They are the angular velocity and the acceleration but how can I do it? the idea is to...
Any spinning item, proton, electron, even planet, has angular momentum that creates force. How can an electron exist in a random orbital cloud around a spinning proton if it has an angular momentum and requires force to alter from any circular orbital plane (like a planet orbiting a star)?
What we know:
The ball is dropped at the tip A with some speed ##v_0## and rebounds with speed ##v##. This collision produces an angular impulse, changing the angular momentum of the bar with the flywheels.
Solution inspired by an answer provided by @TSny in the similar question.
Angular...