An experimentor stands on a stool capable of rotating about a vertical axis and holds a rotating wheel of moment of intertia `I_(1)` about its axis and angualr velocity `epsilon_(1)` with its axis coinciding with the vertical axis of the stool. The moment of inertia of the stool and the experiment about the vertical axis is `I_(2)`. Calculate the change in kinetic energy of the system if the experiment rotates the wheel through
i) `180^(@)` and ii) `90^(@)`

Answer

`(2I_(1)^(2)omega_(1)^(2)//I_(2)), (I_(1)^(2)omega_(1)^(2))/(2(I_(2) + I_(1)/I_(2)))`