Rotational Motion Graphs

Graphs of rotational motion visualize rotation over time. An angular position-time graph plots the angular coordinate $\theta$ against time $t$. For uniform rotation, the graph is a straight line. The slope of this line represents the constant angular velocity $\omega$. A steeper slope indicates a faster rotation rate.

$$\omega = \frac{\Delta \theta}{\Delta t}$$

An angular velocity-time graph displays the angular velocity $\omega$ on the vertical axis and time $t$ on the horizontal axis. For an object rotating at a constant rate, the graph appears as a horizontal line. The rectangular area bounded by the line and the time axis represents the total angular displacement $\Delta \theta$.

$$\Delta \theta = \omega \cdot \Delta t$$

These geometric features connect kinematic quantities. Calculating the slope of the angular position graph yields the velocity. Conversely, calculating the area under the angular velocity graph yields the displacement.