Two wheels, each of moment of intertia 4 kg. `m^(2)`, rotate side by side at the rate of 120 rpm and 240 rpm in opposite directions. If both the wheels are coupled by a light shaft so that they now rotate with a com on angular speed, find this new rate of rotation.

Explanation

Data : I = 4 kg. ` m^(2) , f_(1) = 120 " rpm" , f_(2) = 240` rpm
Initially ,the angular velocities of the two wheels ` (bar(omega_(1) and bar(omega_(2))`)and therefore, their angular momenta (`barL_(1) and barL_(2))` are in opposite direction.
THe magnitude of the total initial angular momentum ` 2I . omega = 4 piI.f`
From Eqs. (1)and (2) , by the principal of conservation of angular momentum.
`4piIf = 2pi I (f_(2) - f_(1))`
`f= (f_(2)-f_(1))/2= (240 -120)/2 = 60 " rpm"`
The gives their new rate of rotation.