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.
I'm sure I've read somewhere that Jupiter has 99% of the solar system's angular momentum, which shouldn't be the case.
However, I can't find a source for this, and any search online for the topic doesn't bring up any science sites.
Did I mis-remember?
Hi,
In my memories there's the information that in a O shaped mounting, the bearings will work in diagonal (the forces will be transmitted following that path).
But in many drawings I can see the presence of a spacer between internal rings. Is it necessary since no force should be transmitted to it?
1)Starting at rest, he brings the weights into his chest. His angular velocity increases.
2)A friend throws a third weight so that the student catches it in one of his outstretched hands. No matter what the direction of the throw, the student's angular velocity decreases.
3) Starting with...
Okay so I actually have the answer because my teacher basically just gave it to me, but I would really like to know why I was even wrong in the first place. Here's my steps:
1. Knowing the momentum transfer per unit area is described by: 1/A dp/dt = S/c. I can begin by relating some known...
I am confused with the following two questions:
1. A particle moves under the influence of a central force directed toward a fixed origin ##O##. Explain why the particle's angular momentum about ##O## is constant.
2. Consider a planet orbiting the fixed sun. Take the plane of the planet's...
Wikipedia says that they are the equivalents of momentum and force in rotational motion but I don't understand why this comparison is possible. The torque's dimension is N*m it seems like energy. What is this energy? Why angular momentum is not mass times angular velocity?
Say we have a motor attached to the Earth with gear A, that drives identically sized gear B. Gear B spins on its own axis and but is also attached to ground. Torque between gears is equal.
Technically each gear has equal but opposite AM right, but If I take Earth into account, how is Ang...
Okay so what I've done;
I've put the diammter d = 1m as r = 1m
The time interval of 4s is t = 4s
and the angular velocitys as;
ω1 = 20 rad/s
ω2 = 40 rad/s
Now to get the accelaration. Angular acceleration can be split into two parts tangetial acceleration and radial acceleration
What I...
In Chapter 4, derivation 15 of Goldstein reads:
"Show that the components of the angular velocity along the space set of axes are given in terms of the Euler angles by
$$\omega_x = \dot{\theta} \cos \phi + \dot{\psi} \sin \theta \sin \phi,
\omega_y = \dot{\theta} \sin \phi - \dot{\psi} \sin...
I am writing an article about the Hubble Tension and when I was looking through the angular diameter distance I get confused over something.
In many articles the angular diamater distance to the LSS defined as the
$$D_A^* = \frac{r_s^*}{\theta_s^*}$$ where ##r_s^*## is the comoving sound...
See attached. You can see how the car as a whole conserves angular momentum with earth. Car pushes back, Earth moves back and rotates, car accelerates forward.
https://www.animations.physics.unsw.edu.au/jw/momentum.html
However, the ground puts a friction force on the front non-driving wheel...
I don’t understand how energy is conserved here. The energy of the atom when n=5 is -.544eV. The energy of the photon is 1.14eV. After release, the energy of the atom is -.544 - 1.14 = 1.68eV. Using this value, I get n = 2.67, not an integer, so n = 3 and the atom has energy = -1.51 eV. I...
I looked in the instructor solutions, which are given by:
But I don't quite understand the solution, so I hope you can help me understand it.
First. Why do we even know we are working with wavefunctions with the quantum numbers n,l,m? Don't we only get these quantum numbers if the particles...
Okay, i know that as a ball collides with a pivoting rod on an axis, the ball has angular momentum. Therefore after the collision, the ball is stopped or slowed, and the rod swings.
The ball provides a force and torque to the rod. But if I isolate the ball, isn't the only thing acting on the...
hello I would like some help with the first part of this homework.
for the moment i have done this:
E initial=m*g*h
Efinal= 1/2 m*v ^ 2+1/2I*ω ^ 2
Ei=m*g*h+1/2I*ω ^ 2
Ef=1/2*m*v ^ 2
my doubt is with the potential energy since it confuses me when there is or not...
Is it correct to say that that τ=0 since r has the same directacion as F??
and for \vec{L} que need to find \vec{p}
So I thought solving this dif equation
## \int dp/dt =−kq/r^2 +β^4/r^5##
Do you agree in the path I am going?
I have the following equation,
$$ C_\ell(z,z') = \int_0^\infty dkk^2 j_\ell(kz)j_\ell(kz')P(k),$$
where $$j_\ell$$ are the spherical Bessel functions.
I would like to invert this relation and write P(k) as a function of C_l. I don't know if this is a well known result, but I couldn't find...
I have seen the solution and understand it. The solution defines θ to be the angle between the falling rod and the table. It then equates initial PE to the final (PE+KE) where the final PE=0 and the final KE to be (1/2) Iω2+ (1/2) ma2ω2 to finally obtain ω = √(3g/2a)
But i would like to know...
I was first wondering wether we can solve this question by applying conservation or energy or not but after googling it I found that we can't apply conservation of energy since there will be some energy lost in this case. I don't know how this energy is getting lost.
My second doubt was if we...
and this is my solution
for question (d), it may seems that $$R=(k)/(k-m\omega^2)R_0$$ so that $$\omega ≠ \omega_i =√(k/m)$$
but $$\omega_c <\sqrt{k/m}$$ is always true, ##\omega_i## corresponds to the limit case when ##F_max## is infinitely large
Besides, I don't know other Physics prevents...
Summary:: Would energy method give us a different answer from conservation of angular momentum?
Hello,
I do not know how to type equations here. So, I typed my question in Word and attached it here. Please see photos.
Note: This question is not a homework. I did not find it in textbooks or...
The Wikipedia page for angular velocity makes a big fuss over "spin" and "orbital" angular velocities, but I have checked through Gregory and Morin's textbooks on classical mechanics and haven't found any reference to them at all. They just work with a single quantity, the angular velocity...
This is a semantic question, without any implications really, but I wondered if someone could check if I understand this correctly? The angular velocity ##\vec{\Omega}## of a frame ##\mathcal{F}## with respect to another frame ##\mathcal{F}'## is defined such that, for any vector...
In which coordinate system the components of angular momentum are quantized? Better to say, if we can select the coordinate system arbitrarily, how the components of angular momentum, say z-component, are always ##L_z=m\hbar##?
Pretty much in a nutshell... fielded a question about how spin affects electron positron annihilation... ie do the spins have to be opposite in order to conserve angular momentum for two-photon annihilation to happen?
Intuitively I figured that looks reasonable ... but decided to check, and...
I was watching the above video which is part of a series explaining the mechanics behind a gyroscope. In the video the author explains the mechanics of the gyroscope when stationary (the disc is not rotating). Here he derives a result that the angular acceleration is g/r which is non zero...
I first tried to get the solution by conserving the rotational kinetic energy and got ##\omega'=\frac2{\sqrt5} \omega##.
But, it was not the correct answer. Next I tried by conserving the angular momentum and got ##\omega'=\frac 45 \omega##, which is the correct answer.
Why is the rotational...
My solutions (attempts) :
a> w=v/r | r=6.35x10^6m | therefore V=7.04x10^-5 m/s
b> speed of rotation is faster at the equator than the pole as w=v/r. As w remains constant, as r increases towards the pole V has to decrease.
c> F = W - R
d> Stuck here. I presume that I have to use the equation...
Angular velocity is the degrees by which something rotates over a time period. If I have an angular velocity in one direction and I resolve it into its components, its components would obviously be of lesser value. Here's what I don't get. When I imagine this scenario, I see that the thing...
Answers are the following :
(i) v=(2cost)i - (2sint)j -(1/2)k
(ii)2.06m/s
(iii)2m/s^2 horizontally towards the vertical axis, making an angle of pi/4 with both the I and j axes.
In this article it discusses the generation of something called super chiral light and claims with metamaterials they can make it have very high angular momentum like l=100. What does that really mean? How does that relate in magnitude to the normally computed linear momentum of a photon p=h/λ...
I am confused because the question implies that I need to do some sort of calculation with Kepler's law. I got
##r+d = \sqrt[3]{\frac{T^2 GM}{4 \pi^2} } ##
But don't understand why I need this, since I already have the distance and the angular diameter should be ##\arctan (2R/d)## I think I...
Hello,
I have this i am learning. I have been trying to find information online but have struggled to find anything which helps me. YouTube usually has good videos, but doesn't seem to on this. This is one topic i have never learned before. But keen to.
I was hoping someone could help me...
Further given:
- every beam is infinite stiff
- pulleys are massless
- cables don't stretch, no slip, and frictionless.
-Every pulley has a diameter D except pulley Q. Pulley Q has diameter 0.5*D
So what I don't understand is how to calculate/determine the velocity at R and S. Can someone help...
IS my solution right? Comparing with the other solutions, the answer just exchange the signals, i don't know why,
THats what ifound.
And here is the three equations:
{i use the point which occurs the collision}
Lo = Lf >>
0 = Iw + M*Vcm(block)
Eg = ct>
mvo² = mvf² + MVcm² + Iw²
I = ml²/3...
The Schwarzschild metric seems to model, for example, the earth’s gravity field above the earth’s surface pretty well, even though the Earth is not really a golf-ball sized black hole down at the center. Can the same be said for the Kerr metric? Does it model a rotating extended body’s gravity...
Hi, I have just joined the forum. Thank you all for being a part of such places so that people like me can get answers to the questions on their minds!
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I have been trying to understand how a quadcopter yaws. Referring to the figure below which is bird's eye view of...
[Mentor Note -- OP deleted his posts after receiving help. His posts are restored below]
@ocean1234 -- Check your messages. Deleting your post is not allowed here, and is considered cheating.
Problem was given: ##\theta(t) = at - bt^2 + ct^4##
a) calculate ##\omega(t)##
b) calculate...
Hi,
I am building a drone for a school project and I am also looking into how it flies. Recently I have been looking into angular momentum, torque, moment of inertia and angular acceleration. However I am struggling to understand moment of inertia and angular acceleration. If possible please...
The centre of mass of the rod would be at the middle of the rod i.e. at
l/2=[50*10^(-2)]/2
The force responsible for torque will be acting downwards = mg
The Torque = mg*l/2*sin(30) =mg*l/4
We know that Torque=I*alpha
Hence alpha = mg*l/(4*I)
Moment of inertia of rod about the end= ml^2/12 +...
Since the equations are, actually, the question, i will post the image with relevant equations here:
it seems strange, I'm almost sure that I didn't make a mistake in the differentiation, but differentiating 9.8b I found 9.7a with both positive terms
θ=90°= π /2 so the instantaneous angular velocity dθ/dt= lim∆ t -> 0 (θ(t + ∆ t)-θ(t))/(∆ t)
When I calculate it out it is π /2 radians per second. Is this correct?