Rotational motion uses angular displacement $\theta$, angular velocity $\omega = d\theta/dt$, and angular acceleration $\alpha = d\omega/dt$. Many linear-motion ideas have rotational analogues.

Torque measures the turning effect of a force: $\vec{\tau} = \vec{r} \times \vec{F}$. Its magnitude is $\tau = rF\sin\phi$, where $\phi$ is the angle between $\vec{r}$ and $\vec{F}$.

Rotational inertia, or moment of inertia $I$, depends on how mass is distributed relative to the axis of rotation. Larger $I$ means more resistance to angular acceleration.

The rotational analog of Newton’s second law is $\sum \tau = I\alpha$. For rolling objects, rotational and translational motions are coupled through the no-slip condition $v = \omega R$.