Relation between linear speed $\"\"$ of an object and angular speed $\"\"$ of the object is $\"\"$ , where $\"\"$ is the radius of the circular motion and $\"\"$ is measured in radians per unit time.

Find the number of revolutions per minute. \ \

Each cable travels at a speed of 9.55 miles per hour, that means $\"\"$ mile/hour.

Diameter of the wheel is $\"\"$ feet.

Radius of the wheel is $\"\"$ feet.

Conversion :

1 foot = 0.000189394 miles.

Convert units from feet to miles :

$\"\"$

Angular speed of a wheel : $\"\"$ .

Consider $\"\"$ .

Substitute he values of $\"\"$ and $\"\"$ in above formula.

$\"\"$

Thus, the number of revolutions per minute is 31.47 rpm.

The number of revolutions per minute is 31.47 rpm.