Tagged Questions
0
votes
1answer
44 views
Calculating the moment inertia for a circle with a point mass on its perimeter
I want to calculate the tensor of the moment of inertia. Consider this situation:
The dot represents a points mass, in size equal to $\frac{5}{4}m$. $m$ is the mass of the homogenous circle. I'm ...
2
votes
1answer
106 views
Questions about angular momentum and 3-dimensional(3D) space?
Q1: As we know, in classical mechanics(CM), according to Noether's theorem, there is always one conserved quantity corresponding to one particular symmetry. Now consider a classical system in a $n$ ...
1
vote
0answers
44 views
Closed-form equation for orientation and angular velocity over time
If a rigid body, rotating freely in 3d, experiences no friction or other external forces and has an initially diagonal inertia matrix $\mathbf{I}_0$ (with $I_{11}>I_{22}>I_{33}>0$) and ...
4
votes
1answer
163 views
Clarifications about Poisson brackets and Levi-Civita symbol
I need some clarifications about Poisson brackets.
I know canonical brackets and the properties of Poisson Brackets and I also know something about Levi-Civita symbol (definition and basic ...
3
votes
1answer
177 views
Can any physical rigid body be represented by an ellipsoid with the same angular dynamics?
According to wikipedia, the inertia tensor of an ellipsoid with semi-axes $a,b,c$ and mass $m$ is
$\left[\begin{array}{ccc}
\frac{m}{5}(b^2+c^2)&0&0\\
0&\frac{m}{5}(a^2+c^2)&0\\
...
1
vote
1answer
328 views
Poisson brackets and angular momentum
I'm trying to find $[M_i, M_j]$ Poisson brackets.
$$\{M_i, M_j\}=\sum_l \left(\frac{\partial M_i}{\partial q_l}\frac{\partial M_j}{\partial p_l}-\frac{\partial M_i}{\partial p_l}\frac{\partial ...
3
votes
1answer
480 views
Conservation of linear and angular momentum
Suppose I have two rigid bodies A and B and they are connected by a spring which is attached off-center (thus possibly causing torques). Due to the spring a force $f$ acts on A and a force $-f$ acts ...
0
votes
0answers
67 views
How to control heavy ball in x and y direction? [closed]
I'm trying to build a device that holds a rather heavy ball and I want to be able to control it's "movement" in the X and Y directions (they are horizontal as well as orthogonal).
My current ...
0
votes
1answer
171 views
Angular momentum conservation in a central field through the Hamiltonian
In my teacher's notes there is a discussion of the Hamiltonian for a central force field with potential $V(r)$.
The Hamiltonian is formulated in spherical polar coordinates:
...
2
votes
1answer
192 views
Angular momentum components as independent integrals of motion
I was told that in order to solve the Kepler problem (6 degrees of freedom in total) you have to proceed, step by step, to reduce those degrees of freedom using the integrals of motion. You do so ...
7
votes
3answers
89 views
Rotationally invariant body and principal axis
Suppose a rigid body is invariant under a rotation around an axis $\mathsf{A}$ by a given angle $0 \leq \alpha_0 < 2\pi$ (and also every multiple of $\alpha_0$).
Is it true that in this case the ...
1
vote
1answer
276 views
Cases in which angular velocity and angular momentum point into same direction
I know that angular momentum $\vec{L}$ and angular velocity $\vec{\omega}$ of a rigid body doesn't point into the same direction in general. However if your body spins around a principal axis, ...
2
votes
2answers
482 views
Conservation of angular momentum in helicopter
I have a small RC-controlled toy helicopter with removable tail rotor.
Suppose I remove the tail rotor, hold the tail with my hand, start the rotor until it moves with constant angular velocity and ...
2
votes
0answers
147 views
Why do control moment gyroscopes exhibit “torque amplification”?
There are a number of articles that describe the benefits of using control moment gyroscopes (CMGs) over reaction wheels in inertial navigation applications. One of the primary benefits of using a CMG ...
1
vote
2answers
265 views
Spin angular momentum of a system of particles : Is there any energy associated with it?
Consider a system of point particles , where the mass of particle $i$ is $μ_i$ and its position vector is $\vec{r}_i$. Let $\vec{r}_\text{cm}$ is the position vector of the center of mass of the ...
1
vote
1answer
598 views
Converting angular velocity to linear velocity through friction
A very basic question here; it's related to this one, but not quite the same.
If a rotating rigid body (a sphere for the sake of discussion) with mass $m$, radius $r$ and inertial tensor $I$ has ...
3
votes
1answer
127 views
Effect of rotation on turbulence threshold for Reynolds number?
If the significance of the Reynolds number is:
Then what is the effect of angular momentum on the transition from laminar to turbulent as in a convective vortex? Waterspouts, in particular, seem ...
5
votes
2answers
738 views
How is angular momentum conserved when a spinning top finally stops spinning?
Where does the top's angular momentum get transferred to? Does it very slightly change the angular momentum of the table, and then the angular momentum of the Earth?
5
votes
1answer
109 views
Sum of angular momentum of all electrons in a magnet
Can the sum of angular momentum of all rotating electrons in all the aligned atoms in a permanent magnet have a significant contribution to the macro angular momentum of the magnet? If yes, why does ...
-1
votes
1answer
540 views
Modeling and Simulating Pendulum Motion
I've been having difficulty creating a mathematical model of a pendulum in my code. While there is plenty of info on general equations describing a the motion of a pendulum, I seem to be having ...
8
votes
2answers
590 views
Intrinsic angular momentum in classical mechanics
Please note, I am only interested in classical mechanics discussion on this. Please do not involve quantum mechanics.
Inspired by this question: Is Angular Momentum truly fundamental?
My question ...
3
votes
2answers
770 views
Dynamics of moment of inertia
I'd like to be able to determine the angular acceleration of a system of two rotating masses, which are connected so as to have a variable mechanical advantage between the two. My background with ...
2
votes
3answers
470 views
How long for a frictionless top to fall over?
We've previously discussed why it is that spinning tops do not fall over, see: Why don't spinning tops fall over?
However, as the highest rated answer notes, the angular momentum of the spinning top ...
3
votes
3answers
798 views
Could life survive a pole shift caused by an asteroid collision?
Could life on earth survive a large pole shift caused by an asteroid collision?
I became aware that there are people who believe that the earth's pole suddenly shifts. That is, its rotational ...
20
votes
6answers
1k views
Rotation angle of a giant lily when a child crawls on its rim
Below is a picture of Giant Water Lily. Scientific Name: Victoria Amazonica. Leaves of some of these could be as big as 3 m diameter and carry a weight of 45kg spread evenly and can support a child. ...
37
votes
9answers
3k views
Is Angular Momentum truly fundamental?
This may seem like a slightly trite question, but it is one that has long intrigued me.
Since I formally learned classical (Newtonian) mechanics, it has often struck me that angular momentum (and ...
1
vote
2answers
266 views
Angular Momentum and Force
I'm stuck on number 5. The answers to the first 4 are correct, but I dont know how to set up number 5. Any idea that I would have would require me having some kind of time information, but thats not ...
1
vote
2answers
1k views
Angular Momentum and Average Torque
Refer to number 6. This is the one I'm stuck on. So angular momentum is conserved right, so initial angular momentum is equal to final angular momentum. Initial is 7.87 so final must be 7.87, right? ...
