Here is a collection of notes on the planar dynamics of rigid bodies. When we say planar dynamics, we are referring to the dynamics of bodies that can only rotate about a single axis (perpendicular to the “plane”). The main relationships are summarized below, followed by rigorous derivations.

Moment equation for a rigid body (derivation here).

Parallel Axis Theorem (derivation here).

Kinetic energy of a rigid body (derivation coming).

Angular momentum of a rigid body (derivation coming).

#### Moment Equation for a Rigid Body Here is a set of notes deriving the rotational equations of motion for the planar dynamics of a rigid body. As usual, we start with Newton’s Second Law. We use rigid body kinematics. Then we write the results in terms of moment of inertia.

#### Parallel Axis Theorem If you know the moment of inertia about the center of mass, then the parallel axis theorem allows you to easily compute the moment of inertia about a different, parallel axis. These notes provide a derivation of the equation that transforms one moment of inertia into the other.