Relation between linear speed $\"\"$ of an object and angular speed $\"\"$ of the object is $\"\"$ , where $\"\"$ is the radius of the circular motion and $\"\"$ is measured in radians per unit time.

Diameter of the wheel is $\"\"$ inches.

Radius of the wheel is $\"\"$ inches.

Conversion :

1 mile = 63360 inches.

1 hour = 60 minutes.

1 minute = 60 seconds.

Convert units from inches to miles :

$\"\"$

Number of revolutions $\"\"$ .

$\"\"$

Convert minutes into hours :

$\"\"$

$\"\"$ .

Angular speed of a wheel : $\"\"$ .

$\"\"$ .

Consider $\"\"$ .

Substitute he values of $\"\"$ and $\"\"$ in above formula.

$\"\"$

Thus, the speed of the road is 37.13 mile/hour.

Find how many revolutions per minute should the balancer be set to test a road speed of 80 miles per hour.

$\"\"$ .

The speed of the road is 37.13 mile/hour.

The number of revolutions per minute should be 1034.3.