Chapter 8: Rotation II: Inertia, Equilibrium, and Combined Rotation/Translation

Definition of rotational inertia

Rotational inertia for point masses, rings, and cylindrical shells rotating about their axes

One-dimensional mass ⇒ differential _________

Two-dimensional mass rotating about an axis perpendicular to its plane ⇒ _________

Two-dimensional mass rotating about an axis contained in its plane ⇒ ___________

Three-dimensional mass ⇒ _________ whose axes lies along the axis of rotation

Area of a ring

Volume of a cylindrical shell

Parallel Axis Theorem

Definition of angular momentum for a point particle

Net angular momentum of a system of particles

Relationship between angular momentum and angular inertia for an extended object rotating about a symmetry axis

Relationship between net torque and angular momentum

It is conserved if the external torque is zero.

It is conserved if the external force is zero.

Object’s Kinetic Energy

A system that is not accelerating

For a point mass, equilibrium is defined by the requirement that __________

Conditions required for equilibrium