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. What is the power required by the engine?
(Note: uniform angular velocity in the absence of friction implies zero torque. In practice, applied torque is needed to counter frictional torque). Assume that the engine is 100% efficient.
The power needed,
P = τ × ω
Where
τ is torque needed to counter friction
ω is angular speed to be maintained
Given,
Torque needed, τ = 180 N m
Angular speed, ω = 200 rad s-1
∴ power required to maintain rotation of 200 rad s-1 by countering frictional torque of 180 N m,
P = 180 × 200
= 36 kW