Question

You are driving up to Portland on I5 when you look down at the speedometer in your car and notice you are driving 65 mph. You remember from the last time you replaced the tires on your car that their diameter was 30 inches. (a) What is the angular speed, in rpm, of your tires as you are driving down the interstate (701 rpm)? If instead you had purchased low profile tires that reduced the tire diameter to 25 inches, by how much would your speedometer be off (13 mph)?

Answer 1

Speed of car = 65 mph = 29.0576 m/s

radius of wheel = 15 inch = 0.381 m

angular speed = speed of car/ radius of wheel = 29.0576/0.381 = 76.267 rad/sec

angular speed in rev/m = 76.267 * 60 / (2*pi) = 728.29 rpm

If 25 inch diameter tires were chosen, then the calculation is as follows:

radius of wheel = 12.5 inch = 0.3175 m

angular speed = 76.267 rad/sec

linear speed = radius of wheel * angular speed = 0.3175 * 76.267 = 24.215 m/s = 54.167 mph

The difference in speedometer reading would have been: 65 - 54.167 = 10.833 mph