# Relation between angular and linear velocity

1. Dec 1, 2011

### anigeo

v=rω.here , what does v(linear velocity) refer to?tangential velocity or radial velocity.further which velocity is responsible for centripetal acceleration?

2. Dec 1, 2011

### chrisbaird

In this case, v is the tangential linear speed. If you were to cut the string that pulls a ball into a circular path, the string would fly off in a straight line at speed v in the direction tangent to the point on the circle where it was when the string is cut (neglecting relativistic effects). For an object in constant circular motion, there is no linear radial velocity. If an object is spiraling in (for instance, you are shortening the string) then it has both a tangential linear velocity and a radial linear velocity.

The angular speed ω is essentially the angular rotation frequency, i.e. the number of times it goes around in a circle per unit time. You can derive and understand the equation you wrote by first convincing yourself using geometry that the length of a circular arc s is just the angle θ it subtends times its radius r:

s = rθ

If you assume constant r and differentiate both sides with respect to time, you end up with your equation relating linear and angular speeds.

3. Dec 2, 2011

### anigeo

Thanks c. Baird . i just got it that there can be no radial velocity as there is no radial displacement.