In the Fig, shown below with what angular speed `'omega'` must 'm' with a radius 'r' rotate on a frictionless table so that 'M' does not move ? (b) If m = 1.0 kg, M = 10.0 kg and r = 0.5 m, find `omega`.

Explanation

(a) Tension in the string = Weight of the hanging mass M.
The tension in the string supplies the required centripetal force to the body of mass m to revolve in a circular orbit of radius r.

`T=mr omega^(2)`
`therefore mr omega^(2)=Mg`
Angular speed,
`omega = sqrt((Mg)/(mr))=sqrt((10xx9.8)/(1xx0.5))=sqrt(196)=14 rad s^(-1)`.