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((10 xx 9.8)/(1 xx 0.5)) = sqrt(196) = 14 "rad"s^(-1)`