Your car\'s speedometer converts the angular speed of the wheels to the linear s

Question

Your car's speedometer converts the angular speed of the wheels to the linear speed of the car, assuming standard-size tires and no slipping on the pavement. If your car's standard tires are 24 inches in diameter, at what rate (in rpm) are your wheels rotating when you are driving at a freeway speed of 30mi/h ? Suppose you put oversize, 30-inch-diameter tires on your car. How fast are you really going when your speedometer reads 30mi/h ? If you now put on undersize, 20-inch-diameter tires, what will the speedometer read when you are actually traveling at 25mi/h ?

Explanation / Answer

d = 24 in = 2 ft w = v / r 30 mph = 44 ft / s w = 44 / 2 = 22 rad /s = 210.08 rpm Clearly the speedometer has been caliberated to show 1 mph...for 7 rpm of the tire... When using 30 in tyre = 2.5 ft tire....v = w*r = 55ft/s = 37.5 mi/h When using 20 inch tire...linear speed = 25 mph...i.e 36.67777ft/ s w = v / r = 36.6777 / 1.6777 = 22 rad /s = 210.08 rpm so reading of speedometer = 210.08 / 7 = 30 mph

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