School & Chat

Angular displacement: The angle through which a rigid object rotates about a fixed axis. By convention, this quantity is positive if the rotation is counterclockwise, negative if it is clockwise. Units are radians (rad).

Radian: An SI unit of angular displacement defined as the circular arc length s traveled by a point on a rotating body divided by the radial distance r of the point from the axis:

In analogy with average linear velocity, average angular velocity ω(t) is the rate of change of angular position:
ω = Δθ / Δt

Since s = rθ, the linear velocity v, which at any position is directed along the tangent to the curve at that point, is proportional to the angular velocity ω:

v = Δs / Δt = rΔθ / Δt = rω

So v = rω