# Questions tagged [rotational-dynamics]

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

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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 ...
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 ...
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, ...
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 ...
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 ...
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 ...
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, ...
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 ...
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 ...
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{\...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...