A merrygoround has a mass of 1430 kg and a radius of 745 m

A merry-go-round has a mass of 1430 kg and a radius of 7.45 m .

Part A

How much net work is required to accelerate it from rest to a rotation rate of 1.00 revolution per 7.50 s? Assume it is a solid cylinder.

Express your answer using three significant figures and include the appropriate units.

Solution

I = 1/2m r² = 0.5 * (1430 kg)(7.45)² = 39684 kgm²

final angular velocity w = Dq/Dt = (1 rev) / (7.50 s)(2p radians/rev) = 0.8378 rad/s

The work will be the rotational kinetic energy E_{k rot} = 1/2 Iw²

= 0.5 * 39684 * 0.8378²

= 13927 J = 1.39 * 10⁴ J