The physics and mathematics of rotating systems.
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.
A simple review of the notation and some of the expressions for kinematics and dynamics along a line, for classical physics.
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.
The description of 2D rotational motion is developed in analogue to linear kinematics.
The description of 2D rotational motion is further developed in analogue to linear dynamics by introducing the rotational equivalents of force, momentum and mass.
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.
A single object or particle moving under the influence of a central force.
Representing rotations by matrices in 2D and 3D
Study of the motion of a spinning solid object with not torques or forces applied.
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.
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.
Equations of motion for a gyroscope are derived by considering the torques.
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.