Angular Velocity



Consider a small body moving a long a circular path. We can describe velocity v the "normal" way, in metres per second. We can also describe it in terms of the angular displacement θ.

This velocity is given by v = s/t, where s is the distance travelled, and t the time taken.

Recall that this is the angle that the line joining the body to the centre of the circle moves through. So we can think of the velocity in radians per second. Then it is called angular velocity, ω. To distinguish the two, we call the other velocity, v, the linear velocity.

The angular velocity is given by ω = θ/t.

They are related in the same way that the distance s and the angular displacement θ are related. Recall that s = rθ, where r is the radius of the circle. Divide this by the time t taken to travel the distance: s/t = rθ/t.

Therefore, v = rω.

The idea of angular velocity can also be used for a large body rotating about an axis in the body. If you turn one full around on the spot in 1 s, then you angular velocity is 2π rad/s.

However, in this case, v is not the velocity of yourself, because you are not going anywehre. Instead, v can refer to the velocity of part of your body, like your finger. Then r would be the distance from your finger to the axis of rotation. Since you are turning on the spot, the axis is most likely the imaginary line from the top of your head through the centre of your body.


Copyright 2010 by Kai Hock. All rights reserved.
Last updated: 22 September 2010.