Question

A truck driver travels at 59 miles per hour. The truck tires have a diameter of 30 inches. What is the angular velocity of the wheels in revolutions per minute (rpm)?

Answer 1

`661.4\ rpm`

Explanation:

we know that

1 mile=63,360 inches

step 1

Find the circumference of the wheels

`C=2\pi r`

we have

`r=30/2=15\ in` -----> the radius is half the diameter

substitute

`C=2\pi(15)`

`C=30\pi\ in`

assume

`\pi =3.14`

`C=30(3.14)=94.2\ in`

Remember that

The circumference of the wheels represent one revolution

Convert 59 miles per hour to inches per minute

`59\ mi/h=59*63,360/60=62,304\ in/min`

using proportion find the number of revolutions

`(1)/(94.2)(rev)/(in)=(x)/(62,304)(rev)/(in)\\ \\x=62,304/94.2\\ \\x=661.4\ rev`

therefore

substitute

`62,304\ in/min=661.4\ rev/min=661.4\ rpm`