A boy is standing on a platform which is free to rotate about its axis. the boys holds an open umbrella in his hand. The axis of the umbrella coincides with tht of the platform. The moment of inertias of the platform plus the boy sytem is `3.0xx10^-3 kg-m^` and that of the umbrella is `2.0xx10^-3` kg-m^2`. The boy starts spinning the umbrella about the axis at an angular speed of 2 rev s1 with respect to himself . Find the angular velocity imparted to the platform.

Explanation

`I+2xx10^-3kg-m^2`
`I=3xx10^-3kg-m^2`
=omega_1=2rad/s`
From the earth reference the umbrella has an angular velocity =`(omega_1-omega_2)`
and the angular velocity of the man will be `omega_2`.
Therefore `I_1(omega_1-omega_2)=I_2(omega_2)`
`rarr 2xx10^-3(2-omega_2)=I_2(omega_2)`
`-2xx10^-3(2-omega_2)=3xx10^-3xomega_2`
`rarr 5omega_2=4`
`rarr omega_2=0.8rad/s`