Question

The Cleveland City Cable Railway had a 14-foot-diameter pulley to drive the cable. In order to keep the cable cars moving at a linear velocity of 14 miles per hour, how fast would the pulley need to turn (in revolutions per minute)

Answer 1

Answer:

13.94 rpm

Explanation:

Given that,

The diameter of the pulley, d = 14 foot

Radius, r = 7 foot

The linear velocity of the pulley, v = 14 mph = 20.53 ft/s

We need to find the angular velocity in rpm.

We know that, the relation between the linear velocity and the angular velocity is as follows :

$v=r\omega\\\\\omega=\dfrac{v}{r}\\\\\omega=\dfrac{20.53}{14}\\\\\omega=1.46\ rad/s$

or

$\omega=13.94\ rpm$

So, the angular velocity of the pulley is 13.94 rpm.