Dynamics of Rigid Body

1. Vector Angular Velocity 

• Concept of vector angular velocity and its existence.

• Explanation of how particle velocities are related within a rigid body.

2. Moments and Products of Inertia 

• Meaning and significance of moment and product of inertia.

• Moment of inertia of a body about any line through the origin of a coordinate frame.

• Radius of gyration and equimomental systems.

• Principal axes and momental ellipsoid.

• Statements of the theorems of parallel and perpendicular axes.

3. General Motion 

• Derivation and interpretation of the equations of motion of a rigid body using the principles of linear and angular momentum.

• Applications of D’Alembert’s principle.

• Explanation of how the motion of the centre of inertia is independent of the motion relative to it.

• Study of angular momentum and kinetic energy of a rigid body rotating about a fixed axis.

• Motion of a rigid body about a fixed axis.

• Study of the compound pendulum and the interchangeability between the point of suspension and the centre of oscillation.

4. Motion of a Rigid Body in Two Dimensions 

• Equations of motion for a rigid body moving in a plane (two-dimensional motion).

• Expressions for kinetic energy and angular momentum about the origin.

• Conditions for pure rolling and sliding motion.

5. Motion Under Impulsive Forces 

• Equations of motion for impulsive forces in two-dimensional motion.

• Conservation laws for linear and angular momentum during impulsive motion.

• Solved problems involving impulse applied to a free rod and a rod rotating about a fixed axis.