An annular metal disc has a mass of 10 kg, inner radius of 4 m, and outer radius of 8m. It is rotating about it's axis passing through centre and perpendicular to the plane. If rotational energy at any instant of this disc is 800 J, how fast (in rpm) it is rotating?

Answer

19.08 to 19.12

Explanation

The moment of inertia of the fly wheel is given `I = 1/2 M(R_(1)^(2) + R_(2)^(2))`
The rotational kinetic energy is `k = 1/2 omega^(2)`.
We slove this for the angular speed:
`omega = sqrt((2K)/(I)) = sqrt((4K)/(M(R_(1)^(2)+R_(2)^(2)))) = 2 rad//sec`.