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.

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

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