Question

a cylinder with a 3 - foot radius spins at a rate of 150 revolutions per minute. to the nearest hundredth, the angular velocity of the cylinder is radians per second

Explanation:

Step1: Convert revolutions to radians

One revolution is $2\pi$ radians. So 150 revolutions per minute is $150\times2\pi$ radians per minute.
$150\times2\pi = 300\pi$ radians per minute

Step2: Convert minutes to seconds

There are 60 seconds in a minute. To get the angular - velocity in radians per second, divide the radians per minute by 60.
$\frac{300\pi}{60}=5\pi$ radians per second

Step3: Calculate the numerical value

$5\pi\approx 5\times3.14159 = 15.71$ radians per second

Answer:

$15.71$