Question

At a museum you can see the four cable lines that are used to pull cable cars up and down a hill. Each cable travels at a speed of 12.65 miles per​ hour, caused by a rotating wheel whose diameter is 6.5 feet. How fast is the wheel​ rotating? Express your answer in revolutions per minute.

Answer 1

54.514 rev/min

Explanation:

Data provided in the question:

Speed of the cable car = 12.65 miles per hour

Diameter of the rotating wheel, d = 6.5 feet

Now,

The speed of rotation of the wheel will be equal to the speed of the cable car

thus,

The speed of rotation of the wheel = 12.65 miles per hour

also,

1 miles = 5280 feets

1 hour = 60 minutes

Thus,

The speed of rotation of the wheel =
`(12.65*5280)/(60)`

= 1113.2 ft/ min

Circumference of the wheel = πd

= 6.5π feet

= 20.42 feet

Therefore,

The speed of rotation of the wheel in revolutions per minute

= 1113.2 ÷ 20.42 rev/min

= 54.514 rev/min