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

line segments

One-dimensional mass ⇒ differential \_________

rings

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

rectangular strips

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

cylindrical shells

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

2πr dr

Area of a ring

(2πr dr)h

Volume of a cylindrical shell

Parallel Axis Theorem

L \= r x p

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

Angular momentum

It is conserved if the external torque is zero.

Linear momentum

It is conserved if the external force is zero.

Object’s Kinetic Energy

Equilibrium

A system that is not accelerating

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

Conditions required for equilibrium