AP Physics C

Radians and Degrees

Typically people discuss rotational motion in terms of degrees, where one entire rotation around a circle is equal to 360°. When dealing with rotational motion from a physics perspective, measuring rotational motion in units known as radians (rads) is much more efficient. A radian measures a distance around an arc equal to the length of the arc’s radius.

Up to this point, you’ve described distances and displacements in terms of Δx and Δy. In discussing angular displacements, you must transition to describing the translational displacement around an arc in terms of the variable s, while continuing to use the symbol θ (theta) to represent angles and angular displacement.

The distance completely around a circular path (360°), known as the circumference, C, can be found using ∆s = C = 2