Question

A car tire has a radius of 15 inches. Suppose the car is traveling at 60 miles per hour (1 mile = 5,280 feet). What is the approximate rate of spin, in revolutions per minute, of the tire? Round the answer to the nearest whole number.

Answer 1

Radius = r = 15 inches
Speed of the car = v = 60 miles per hour
= 60 x 5280 feet per hour
= 316800 feet per hour
= 316800 x 12 inches per hour
= 3801600 inches per hour
= 3801600/60 inches per minute
= 63360 inches per minute

Angular velocity = w = ?

v = r w 
w = v/r

So,

w = 63360/15
= 4224 radians per minute
= 4224/2π revolutions per minute
= 672 revolutions per minute

So, the angular velocity of the tire is 672 revolutions per minute

Answer 2

First find the distance covered in 1 revolution,
Circumference  = 2π×15/12 = 7.85398 feet.              (1 foot=12 inches)

7.85398 feet = 7.85398/5280 = 0.001487496522 miles 

In 1 hour, it travels 60 miles. This means it travels (60/60) miles in 1 minute.

So, it travels 1 mile in 1 minute.

The rate of rotation = 1/0.001487496522
                               = 672.27rpm

To the nearest whole number = 672 rpm