Supercharge your learning!

Use adaptive quiz-based learning to study this topic faster and more effectively.

Angular displacement

An object moving in circular motion traces the arc of a circle. The angle between the radii at the beginning and the end of the arc (the angle subtended by the arc) is the angular displacement $$(\theta)$$ of the object.

This is given by $$\vecphy{\theta}=\frac{\vecphy{s}}{r}$$, where $$s$$ is the arc length and $$r$$ is the radius of the arc.

Angular displacement can be thought of as a vector, but for simplicity it is usually considered to be a scalar.

The SI unit of angular displacement is the radian $$(\text{rad})$$. One radian is $$180/\pi$$ degrees.

The angular displacement can exceed $$2\pi\text{ rad}$$, which means that more than one revolution has been completed. The angular displacement can therefore be thought of as an angular "distance."

An object moving in uniform circular motion with angular displacement <span style=$$\vecphy{\theta}$$, angular velocity $$\vecphy{\omega}$$, velocity $$\vecphy{v}$$ and radius $$r$$" src="https://www.toktol.com//Content/images/transparent.gif" onload="conditionalLoadImage(this, 'https://toktolweb.blob.core.windows.net/courseimages/', 'Physics.AL.NM.CM.01.png', false, {}, 'https://toktolwebcdn.blob.core.windows.net/quizimages/')" name="Physics.AL.NM.CM.01.png" sub="An object moving in uniform circular motion with angular displacement $$\vecphy{\theta}$$, angular velocity $$\vecphy{\omega}$$, velocity $$\vecphy{v}$$ and radius $$r$$" />
An object moving in uniform circular motion with angular displacement $$\vecphy{\theta}$$, angular velocity $$\vecphy{\omega}$$, velocity $$\vecphy{v}$$ and radius $$r$$