Question

If a car has tires with a diameter of 28 inches and is traveling at 55 mph, how fast are its tires spinning, in rpm^ prime s (revolutions per minute)? [There are 63,360 inches in 1 mile) Round your final answer to 2 decimal places .

Answer 1

The tires are spinning at 660.49 revolutions per minute.

Explanation:

The speed of the tires (v) is the same that the speed of the car, so to find the angular velocity of the tires we need to use the equation:

`\omega = (v)/(r)`

Where:

r: is the radius of the tires = d/2 = 28 inches/2 = 14 inches

`\omega = (55 mph)/(14 inches*(1 mile)/(63360 inches)) = 2.49 \cdot 10^(5) (rad)/(h)*(1 h)/(60 min)*(1 rev)/(2\pi rad) = 660.49 rpm`

Therefore, the tires are spinning at 660.49 revolutions per minute.

I hope it helps you!