Question

a 95 - 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: Know the number of radians in one - revolution

One revolution is equal to $2\pi$ radians.

Step3: Calculate the angular speed

The propeller rotates at 4600 revolutions per minute. First, convert the time - unit from minutes to seconds. The number of revolutions per second is $\frac{4600}{60}=\frac{230}{3}$ revolutions per second. Then, since each revolution is $2\pi$ radians, the angular speed $\omega$ in radians per second is $\omega=\frac{230}{3}\times2\pi$.
$\omega=\frac{460\pi}{3}\approx481.7$ radians per second.

Answer:

$481.7$