An engine needs to transmit a steady torque to maintain a rotor at a uniform angular speed. If the e

Question

An engine needs to transmit a steady torque to maintain a rotor at a uniform angular speed. If the engine is $100\%$ efficient, operates at a power of $36	ext{ kW}$, and applies a torque of $180	ext{ Nm}$, what is the uniform angular speed of the rotor?

Professor PC Thomas Classes · Answer

The power $P$ associated with torque $	au$ and angular velocity $\omega$ in rotational motion about a fixed axis is given by $P = 	au\omega$. Substituting the given values: $36000	ext{ W} = 180	ext{ Nm} 	imes \omega$. Solving for $\omega$ gives $\omega = \frac{36000}{180} = 200	ext{ rad/s}$.