Rotational dynamics

When a body does not merely translate but rotates, a new quantity comes into play: the moment of inertia. Rotational dynamics is the exact analogue of translational dynamics, with torque replacing force and moment of inertia replacing mass. This chapter builds the analogy step by step — angular acceleration, moment of inertia, Newton’s second law for rotation — then tackles massive pulleys, rolling bodies, conservation of angular momentum and the famous problems of the projectile against a rod and the billiard ball. It lays the groundwork for gravitation: the same force that makes an apple fall keeps the Moon in orbit.

Sections

• Angular acceleration
• Moment of inertia
• Newton’s second law for rotation
• Pulleys with mass
• Double-radius pulley
• Rolling bodies
• The complete translation–rotation analogy
• Conservation of angular momentum
• Projectile against a rod: three cases compared
• Collisions in two dimensions
• The billiard ball: where to strike?

Reflections

• The translation–rotation symmetry
• Moment of inertia: a mass with a memory of shape

Exercises

• All worked exercises of the chapter