Your car\'s speedometer works in much the same way as its odometer, except that

Question

Your car's speedometer works in much the same way as its odometer, except that it converts the angular speed of the wheels to a linear speed of the car, assuming standard-size tires and no slipping on the pavement.

Part A

If your car has standard 24.0inch -diameter tires, how fast are your wheels turning when you are driving at a freeway speed of 73.0mph ?

Part B

How fast are you going when your wheels are turning at 520rpm ?

Part C

If you put on undersize 18.0inch -diameter tires, what will the speedometer read when you are actually traveling at 47.0mph ?

Explanation / Answer

1. 1022.92 RPM
2. 37.109 MPH
3. 62.66 MPH

This is just a conversion problem. 1 mile is 63360 inches. 1 hour is 60 minutes. pi*diameter is circumference.

Part 1:
(63360 in / mile)*(73 miles / hr)*(1 rotation / 24*pi in)* (1 hr / 60 min) = 1022.92 rotations / min

Part 2:
(520 rotations / min)*(60 min / hr)*(pi*24 in / rotation)*(1 mle / 63360 in) = 37.109 miles / hour

Part 3:
First, find the actual RPM of the car
(47 miles /hr)*(1 rotation / pi*18 in)*(63360 in / mile)*(1 hr / 60 min) = 878.13 rotations / min
Then convert it to MPH assuming the wheels are 24 inches:
(878.13 rotations / min)*(pi*24 in / rotation)*(1 mile / 63360 in)*(60 min / hr) = 62.66 miles / hr

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