Question

You are driving your car at 55 mph (24.6 m/s). Your car has 15-inch radius tires (1 inch = 2.54

cm). What is the angular speed of the tires?

Answer 1

To find the angular speed of the tires, we need to use the formula:

angular speed = linear speed / radius

First, we need to convert the speed from miles per hour to meters per second, and the tire radius from inches to meters:

55 mph = 24.6 m/s (approximately)

15 inches = 15 x 2.54 cm/inch = 38.1 cm = 0.381 m

Now we can calculate the angular speed:

angular speed = linear speed / radius
angular speed = 24.6 m/s / 0.381 m
angular speed = 64.6 radians/second (approximately)

Therefore, the angular speed of the tires is approximately 64.6 radians/second.