Question

A bicycle with 24 inch diameter wheels is traveling at 12 mi/h. Find the angular speed of the wheels in radians per minute.

Answer 1

1056 radians/min

Explanation:

We can convert the linear speed to inches per minute to help with finding the angular speed.

(12 mi/h) = (12 mi)(5280 ft/mi)(12 in/ft)/((1 h)(60 min/h))

= (12×5280×12/60) in/min = 12,672 in/min

Each radius-length represents 1 radian of arc of the wheel. The radius is half the diameter, 24 in/2 = 12 in, so the angular speed is ...

(12,672 in/min)/(12 in/radian) = 1056 radians/min