# Conservation of angular momentum

1. ### MechatronO

27
Imagine a body that is attached to a massless string and then rotated in such a manner that no external forces like gravity acts on the body in tangential direction.

The body now has the angular momentum with respect to the axis of rotation

Lo = Ro * Vo * m

Where

Ro = constant initial radius of rotation
Vo = constant initial tangential velocity
m= mass of the body

If the string is pulled in with respect to time, and no torque is applied with respect to the axis of rotation would the velocity be this, according to the law about conservation of angular momentum?

V(t)=$\frac{Vo*Ro}{r(t)}$ ?

And would the tangential acceleration then be

a(t)=$\frac{-Vo*Ro}{(r(t)^2)}$*r(t)' ?

Where

r(t)´ = the derivate of the radius of rotation with respect to time

If so, could this acceleration be added directly to external forces that is causing tangential acceleration?

The purpose is forwarding a regulator that will control the acceleration of a robot.

### Staff: Mentor

Looks right.
External forces could change r'(t), but if they do not, I would expect that you can add them.