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

Answer:

$661.4\ rpm$

Step-by-step 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  

$\frac{1}{94.2}\frac{rev}{in}=\frac{x}{62,304}\frac{rev}{in}\\ \\x=62,304/94.2\\ \\x=661.4\ rev$

therefore

substitute

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