Worked example 8.6: Horsepower of engine

Question: A car engine develops a torque of $\tau=500 {\rm N m}$ and rotates at $3000 {\rm rev./min.}$. What horsepower does the engine generate? ( $1 {\rm hp} = 746 {\rm W}$).

Answer: The angular speed of the engine is

$$\omega = 3000\times 2 \pi/ 60= 314.12 {\rm rad./s}.$$

Thus, the power output of the engine is

$$P = \omega \tau = 314.12\times 500 = 1.57\times 10^5 {\rm W}.$$

In units of horsepower, this becomes

$$P = \frac{1.57\times 10^5}{746} = 210.5 {\rm hp}.$$