Questions tagged [rotational-dynamics]

A tag for questions about the mechanical interactions of rotating objects, including torque and angular momentum.

355 questions with no upvoted or accepted answers
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15
votes
2answers
793 views

Bottle stability optimization

A few days ago some friends and I played a game called "flunkeyball" where you need to upset a bottle with a ball. Then a question occurred: "How much water do we need to put into the bottle that its ...
8
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2answers
543 views

General motion of a cone on an inclined surface

Suppose that a solid cone is placed horizontally on an inclined surface and is initially at rest. How will the cone move when it starts motion due to its weight? I know that its motion depends on the ...
6
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0answers
203 views

How can I approximate Jacobian Elliptic Functions in terms of basic integrable functions for the SO(3) rotation of a rigid body?

So, the rotation of a 3d body can be described with Euler's equations of motion giving the rotational velocity in components along the principal axes of inertia. As showed in f.ex. this paper, ...
5
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1answer
718 views

What is the problem of having an inertia tensor not satisfying the triangle inequality?

It is well known that rigid body inertia tensors are 3 by 3 positive semidefinite matrices, which is the same as saying that their eigenvalues are all non-negative. A little less known is the fact ...
5
votes
1answer
583 views

Lagrange: when a potential force, when a generalized force?

Consider the following case of a drum unrolling a mass that is on a massless string wrapped around the drum: According to my professor, here we must consider the mass $m$ being in a gravitational ...
5
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1answer
392 views

Sum of energy for 2 solids in rotation

I would like to compute the sum of energy of the following case: Two solids are turning (disks). Yellow solid is turning at $w_1$ radians per second around its center of gravity and blue solid is ...
5
votes
1answer
345 views

Protoplanetary disks, angular momentum and prograde orbits

Very similar question at Astronomy SE: https://astronomy.stackexchange.com/q/6183/4042 Given a typical protoplanetary disk made up of the usual planetary system stuff, dust and gas and whatnot, ...
5
votes
1answer
152 views

Taking pivot about an accelerating point

Given this question: A small ball of mass $m$ and radius $r$ rolls without slipping on the inside surface of a fixed hemispherical bowl of radius $R>r$. What is the frequency of small ...
4
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0answers
43 views

Does an object with an axially symmetric inertia tensor have a “preferred” axis of rotation?

Imagine an object with cylindrical symmetry, such as a cylinder or cylindrical shell, where $I_{xx} = I_{yy} \neq I_{zz}$, and the Z axis is defined along the length of the cylinder shape. The object ...
4
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0answers
28 views

Fixed coordinate frame as limit of rotating coordinate frame

I have a question about a fixed coordinate system as limit of rotating system. Consider for example a pendulum. The Lagrangian in the rotating frame is given by \begin{equation} L(\mathbf{r}, \mathbf{\...
4
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1answer
40 views

Deriving equations of rotational motion for connected rods

I'm working on a problem involving deriving equations of rotational motion for a system of connected rods (see the picture), and I'm a bit confused about a few things to do with rotational motion. I ...
3
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0answers
50 views

Concept of polarization in microwave rotational spectroscopy

I am trying to understand the concept of polarization of molecules after they are excited by a microwave pulse. The context is: The complexes are produced in a pulsed supersonic jet expansion of a ...
3
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0answers
315 views

Start of gyroscopic precession

Let's consider the classical example, the wheel hung by one side of the axle: ¹ When the wheel is not spinning, it will tilt down the free end of the axle first. When the wheel is spinning, it will ...
3
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1answer
613 views

Circular motion, kinetic friction and tension

Hi: I've read this post: Uniform Circular Motion w/ Tension and Friction and helped me a lot. I have a similar problem: At one end of the rope ($R = 1 m$) is tied a mass ($m = 3 kg$) and the ...
3
votes
2answers
426 views

Precession on a heavy rod: Angular momentum and torque contradiction

Say I got a so massive rod and a relatively light spinning flywheel. Fixing an end on a pivot, and the disk on the other endpoint, as expected, the rod would undergo precession. If we call the plane ...
3
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0answers
415 views

Rotating a Gaussian Beam

I need to see how the phase fronts of two gaussian beams interact when they intersect with each other. The two beams are tilted towards each other so that they intersect each other at their respective ...
3
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0answers
624 views

3 Axis Gyroscope with forced Precession and Limits of Motion

I am working a problem concerning a 3 axis gryoscope, the spinning mass is a magnet (dipole). This is part of a optical sensing device. The inner gimbal is for pitch rotation, and the outer gimbal is ...
3
votes
1answer
3k views

Neglecting friction on a pulley?

So, this is how the problem looks: Plus, the pulley is suspended on a cord at its center and hanging from the ceiling. You're given masses of the objects, mass of the pulley and it's radius. And ...
3
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0answers
383 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 ...
3
votes
1answer
127 views

Does rotation happen throughout the whole x axis of an object simultaneously?

For example, if I draw a line on the side of a pencil top to bottom, then snap one end of it as in launching it due to the pressure of my fingers. Anyways, if I record the pencil launch in slow motion ...
2
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2answers
75 views

Why does a chain or rope move the way it does when suspended and rotated on a horizontal axis?

I have always been interested in why objects like chains, ropes, etc. move the way they do when "rotated" around a vertical axis while being held only where it is suspended. It forms a shape if you ...
2
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0answers
52 views

How does friction cause a spinning top to fall?

I am wondering how friction can create a torque to change the angular momentum and cause a spinning top to tilt, like in the diagram of a close up of the rounded tip of a top while the angular ...
2
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0answers
34 views

Reaching a desired orientation under constant angular momentum

For a rigid body with a given inertia tensor, and a target orientation and time, how can I determine a constant angular momentum that will move the body to the target orientation? I see this could be ...
2
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0answers
32 views

Parallel Axis Theorem and Kinetic Energy of the Earth

I'm looking for a little clarification on the parallel axis theorem and computing the total kinetic energy of the Earth in it's orbit round the Sun. So the Parallel Axis Theorem states that $I = I_{...
2
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1answer
84 views

How $ d \vec s = d \vec \theta × \vec r $

Here:- $ d \vec s $ = infinitesimal linear displacement, $ d \vec \theta $ = corresponding infinitesimal angular displacement, $\vec r $ = radius vector I am trying to understand the proof of work ...
2
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1answer
77 views

Calculating acceleration of end point of rod

Suppose I have a rod hinged at its end, of length $\ell$ free to rotate about an horizontal axis; initially in the horizontal position and I have to calculate the acceleration of its other end point. ...
2
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0answers
45 views

Why does the parallel axis theorem apply in this case?

Next, the wheel is flipped over, so the angular momentum of the wheel is now negative. Obviously, the person must start rotating counterclockwise to conserve angular momentum. Since the person is ...
2
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0answers
97 views

Rotational potential energy on a system of two masses

On a homework assignment, we were given the following problem: This system is held at equilibrium according to the configuration in the image; initially the body B is at rest, and the body A is ...
2
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0answers
95 views

Time derivative in rotating frame

In Goldstein (2ed) sec 4.9 - Rate of change of a vector, why does he say that the instantaneous angular velocity $\omega$ is not a derivative of any vector? $$ (d\textbf{G})_{space} = (d\textbf{G}...
2
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2answers
535 views

Difference between torque, moment and couple

I know the basics of them like Torque is force multiplied by the distance (from the point where there is no rotation like centre of gravity). Couple acts because of two equal and opposite forces ...
2
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1answer
569 views

The dynamics of a cornering wheel

Can a rolling wheel create a side force without first rotating on a vertical axis? There is something wrong with the way we describe how a cornering vehicle wheel creates a cornering force. I think ...
2
votes
1answer
62 views

Does LIGO accounts for Sagnac effect?

After reading Sagnac effect one thing immediately come to my mind is LIGO, I only read that the team building LIGO have already considered the curvation of Earth surface but what about Earth's ...
2
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0answers
67 views

What are the fundamentals of motion in a non-inertial reference frame?

First of all, note that I understand what is considered off and on topic here. I'm posting this because I likely lack some sort of conceptual understanding of motion in non-inertial reference frames, ...
2
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1answer
58 views

why do two balls in a bottles separate when the bottles is rotated?

When you rotate a bottle which has only one ball inside the ball moves to one end of the bottle. However in case of two balls both the balls move to different ends. The people that I have asked have ...
2
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0answers
70 views

Stress tensor associated with centrifugal/centripetal load

I have some trouble to understand the relationship between internal stress tensor and the external traction force (in this example, the traction force is a volumic centripetal force). Consider a cube ...
2
votes
1answer
490 views

Does angular momentum depend on coordinate frame?

I am working through a problem and getting what seems to be different answers in different reference frames. The angular momentum of a point mass with respect to an axis that doesn't go through the ...
2
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0answers
257 views

Dynamics of a Gyroscope motion

If we take a gyroscope with a spinning rotor and rotate the gyroscope frame about a vertical axis or the spin axis (see reference figure), we notice that the gimbal+rotor flips about the gimbal axis. ...
2
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0answers
40 views

Thermal fluctuations in orientation of point particles

I am modeling group of point particles with 6 degrees of freedom each - 3 positional degrees of freedom and 3 orientational degrees of freedom. So, each particle has 3 position coordinates and a unit ...
2
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0answers
284 views

Dzhanibekov effect in quantum systems

Dzhanibekov- or Tennis racket effect is what happens when an object with three diferent moments of inertia doesnt spin around the axis with highest or lowest moment of inertia. The object starts to ...
2
votes
1answer
168 views

Effect of forces inside a sphere

What would be the effect of applying two parallel forces of the same value at opposite points of the equator inside a sphere? Common sense tells me that it wouldn't move, but it seems that it could ...
2
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0answers
82 views

centrifugal acceleration and circular velocity in curved space time

I'm studying a problem on rotation systems in general relativity. I would like to know how do these two well know newtonian formulas: $$a_{c}(r)=\dfrac{V_{c}^{2}(r)}{r},\\-\:\dfrac{\partial\Phi(r)}{\...
2
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0answers
446 views

Relation between inertia tensor and moment of inertia about an axis

As far as I understood, we define two quantities: Inertia Tensor - a $3\times3$ matrix, which describes the object "mass" of rotation in relation to a certain point, helping us calculating rotations ...
2
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0answers
60 views

Supersonic object in circular motion?

I was wondering, what would happen if a person was to stand at the center of a circumference of radius $R$, where a loudspeaker playing a musical note in the audible range ($C_5=523 Hz$ for example) ...
2
votes
2answers
415 views

Table saw kickback momentum

When using a table saw, the operator needs to be very careful to avoid kickback. This is where the the teeth on the far side of the rotating blade lift the stock (eg a piece of wood) off the table and ...
2
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0answers
76 views

What happens when a planet's core freezes?

We know the Earth's interior is differentially rotating -- the core is rotating much more quickly than the crust. This is possible because the outer core is liquid and is presumably low enough ...
2
votes
1answer
151 views

What happens when one uses a blender in zero gravity?

I was recently told by a friend that using a blender type apparatus in a zero gravity environment will act like a centrifuge instead mixing properly. Is this the case? Furthermore, can anyone provide ...
2
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0answers
779 views

Calculating torque required to keep an object rotating

I am hoping someone can help me clear up my understanding on rotational dynamics. In particular, how to determine the torque required to keep an object rotating. My understanding (please tell me if ...
2
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0answers
159 views

Precession of angular momentum vector

I'm studying Classical Mechanics on Goldstein's book, so I'm using his terminology and notation. First I'll explain where the question comes from: consider a heavy symmetrical top and consider the ...
2
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0answers
488 views

Autocorrelation function corresponding to density of states with significant rotational motion

Most statistical physics textbooks (at least the ones I've found) state simply that the density of states of a system can be found as the temporal Fourier transform of the velocity autocorrelation ...
2
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0answers
2k views

Degeneracy of Rotational Energy Levels of a Diatomic Molecule

To derive the energy levels of a diatomic molecule (with the z axis the axis of symmetry of the molecule), we write the Hamiltonian as $$H=\frac{1}{2}(\frac{L_x^2}{I}+\frac{L_y^2}{I}+\frac{L_z^2}{I_z})...