Angular Variables

To describe rotational motion, we introduce angular quantities.

Angular Displacement

Angular displacement measures the angle through which a body rotates.

$$ \theta = \frac{s}{r} $$

Where:

• $s$ = arc length
• $r$ = radius

Angular Velocity

Angular velocity is the rate of change of angular displacement:

$$ \omega = \frac{d\theta}{dt} $$

Angular Acceleration

Angular acceleration is:

$$ \alpha = \frac{d\omega}{dt} $$