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# 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."

$\vecphy{\theta}$, 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 $r$