To maintain a rotor at a uniform angular speed of 200 rad s^–1, an engine needs to transmit a torque of 180 N m. The power required by the engine. Assume that the engine is 100% efficient.
 

The rotor's angular speed is 200 rad/s.
The engine must be able to deliver 180 Nm of torque.

The rotor's necessary power for energy transmission to apply a torque τ and rotate a motor with an angular speed ω

$\mathrm{P}=\mathrm{\tau \omega } =180\times 200\mathrm{W} =36\mathrm{kW}$

Hence the correct answer is 36kW.