An automobile engine develops $100 ext{ kW}$ of power when rotating at a speed of $1800 ext{ rev/m

Question

An automobile engine develops $100	ext{ kW}$ of power when rotating at a speed of $1800	ext{ rev/min}$. What torque does it deliver?

Professor PC Thomas Classes · Answer

Power $P = 	au\omega$. Given $P = 100	ext{ kW} = 100,000	ext{ W}$ and angular velocity $\omega = 1800	ext{ rev/min} = 1800 	imes \frac{2\pi}{60} = 60\pi	ext{ rad/s}$. Therefore, torque $	au = \frac{P}{\omega} = \frac{100,000}{60\pi} = \frac{5000}{3\pi}	ext{ Nm}$.