A merry-go-round has a mass of 1600 kg and a radius of 8.00 m .

Question

Part A How much net work is required to accelerate it from rest to a rotation rate of 1.00 revolution per 8.60 s ? Assume it is a solid cylinder.

W= j

Answer 1

If we calculate the final rotational kinetic energy, we will have the net work required.

The rotation kinetic energy is given by 1/2 x I x ω².

the moment of inertia, I, for a solid cylinder is 1/2 x mass x R² where R is the radius.

I = 1/2 x 1600kg x 8.0m² = 51200 Kgm².

ω must be in radians per second, so ω = 1 rev/8.60 s x 2π rad/rev. = 0.730 rad/s.

The K_rot = 1/2 x 51200 Kgm² x 0.730 rad/s² = 13.642 joules (this neglects any work lost to friction).