Constant Angular Acceleration

The linear kinematic equations come from integrating a constant acceleration twice: once to get velocity, once more to get position. Rotational motion follows the exact same logic, because angular position, angular velocity, and angular acceleration are defined by the same calculus relationships as their linear cousins, just measured in radians instead of meters. If alpha is constant, integrating it once gives omega = omega₀ + alpha t, and integrating again gives theta = theta₀ + omega₀ t + (1/2) alpha t^2. Combine those two to eliminate t and you get omega² = omega₀² + 2 alpha(theta - theta₀). Same structure, new letters, same reason it works.

Because the equations are structurally identical, you solve rotational problems exactly like linear ones: identify what you know, pick the equation missing the unknown you don't care about, and solve. Revolutions are just angle in radians divided by 2 π, so converting between the two is a unit step, not a new concept.

This topic is the foundation for the rest of the unit. Once you can describe how fast something spins and how that spin rate changes, you're ready to ask why it changes, which is where torque, moment of inertia, and the rotational version of Newton's second law come in.