The physics and mathematics of rotating systems.
Level: 2, Subjects: Classical

This thread supports half of a first year advanced physics course at Macquarie University. We examine in some detail the physics of rotating systems and objects.

Status: Many of lectures are typeset but no exercises yet. Supporting material as mindmaps available on link below

Mindmaps: /map/rotational-dynamics/. Many of the maps are 10Mb or more so please be patient. Scroll to zoom, click and drag to pan or otherwise use the controls on the side.

Curriculum:

1 Linear Motion  

1 Review of Linear Motion

A simple review of the notation and some of the expressions for kinematics and dynamics along a line, for classical physics.

1 Linear Motion  

2 Centre of Mass

The centre of mass of a system of particles is derived as a fictitious point that behaves as if the mass of the entire system where concentrated there. Tricks for finding it are discussed.

1 Rotation Dynamics  

3 2D Rotational Kinematics

The description of 2D rotational motion is developed in analogue to linear kinematics.

1 Rotation Dynamics  

4 2D Rotational Dynamics

The description of 2D rotational motion is further developed in analogue to linear dynamics by introducing the rotational equivalents of force, momentum and mass.

2 Rotation Dynamics  

5 Rotating coordinate system

In a rotating coordinate system, a free particle moves in a way that appears to be affected by three forces: the centrifugal force, the Coriolis force and the Euler force. These forces arise only from the rotation of the coordinate system.

2 Central Forces  

6 Central Forces

A single object or particle moving under the influence of a central force.

1 Rotation  

7 Rotation Matrices

Representing rotations by matrices in 2D and 3D

2 Rotation Dynamics  

8 Torque Free Motion

Study of the motion of a spinning solid object with not torques or forces applied.

2 Rotation Dynamics  

9 Stability of Rotation

Given an object spinning around some axis with no external torques applied, how stable the rotation is depends around which principal axes the rotation is close to.

2 Rotation Dynamics  

10 The Square Cat

An extremely simplified model of a cat (just four masses!) is presented, following Putterman and Raz [Am. J. Phys. 76, 1040 (2008)]. This simple model is enough to show how a deformable body is able to rotate itself despite conserving angular momentum.

2 Rotation Dynamics  

11 Gyroscopic Motion

Equations of motion for a gyroscope are derived by considering the torques.

2 Rotation Dynamics  

12 Heavy Symmetrical Top

The equations of motion for a heavy symmetrical top are derived in terms of the Euler angles and using a Lagrangian approach. The solutions are examined numerically.