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.

In the Fig, shown below with what angular speed 'omega' must 'm' with

1.	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.
Answer» Solution :(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)`.