Question

a 100 - horsepower outboard motor at full throttle will rotate its propeller at exactly 4600 revolutions per min. find the angular speed of the propeller in radians per second. 4600 rev per min ≈ □ radians per sec (round to the nearest tenth as needed.)

Explanation:

Step1: Convert minutes to seconds

There are 60 seconds in 1 minute.

Step2: Recall the conversion of revolutions to radians

1 revolution = $2\pi$ radians.

Step3: Calculate angular - speed

The propeller rotates at 4600 revolutions per minute. First, convert the number of revolutions per minute to revolutions per second: $\frac{4600}{60}$ revolutions per second. Then, convert revolutions per second to radians per second. Since 1 revolution = $2\pi$ radians, the angular speed $\omega$ in radians per second is $\omega=\frac{4600}{60}\times2\pi$.
$\omega=\frac{4600\times2\pi}{60}=\frac{920\pi}{6}=\frac{460\pi}{3}\approx481.7$ radians per second.

Answer:

$481.7$