The Rotational Kinematic Equations

Spinning motion and straight-line motion obey the same underlying pattern, because an angle is just a position measured in radians instead of meters. A point on a spinning wheel moves the same way a car moves down a road, except its position is described by how far it has rotated. So every equation from Unit 1 survives, letter for letter, once you relabel the variables.

The mapping is one-to-one. Position x becomes angle theta. Velocity v becomes angular velocity omega. Acceleration a becomes angular acceleration alpha. Time t stays time. So v = v0 + at becomes omega = omega0 + alpha t. And x = x0 + v0 t + (1/2) a t² becomes theta = theta0 + omega0 t + (1/2) alpha t^2. The same constant-acceleration restriction applies: these equations only work when alpha is constant, exactly like the linear versions only worked when a was constant.

This topic is the gateway into the rest of the unit. Once angle, angular velocity, and angular acceleration are defined and related by these equations, the next step connects alpha to torque and rotational inertia the same way Unit 2 connected a to force and mass. Every trick you learned for constant-acceleration problems — picking the right equation, using average velocity, solving for time first — carries over directly, just with new symbols attached to the same logic.