Part A.If the car has standard 24.0 inch-diameter tires how fast are the wheels

Question

Part A.If the car has standard 24.0 inch-diameter tires how fast are the wheels turning when you are driving at the speed 69.0 mph?b)how fast are you going when your wheels are turning at 590 rpm?c)If you put on undersize 18.inch-diameter tires,what will the speedometer read when you are actually traveling at 48.0 mph? Part A.If the car has standard 24.0 inch-diameter tires how fast are the wheels turning when you are driving at the speed 69.0 mph?b)how fast are you going when your wheels are turning at 590 rpm?c)If you put on undersize 18.inch-diameter tires,what will the speedometer read when you are actually traveling at 48.0 mph?

Explanation / Answer

Here ,

a) speed , v = 69 mph

radius , r = 24/2 inch = 1 feet

r = 0.3048 m

69 * 1609/3600 = 0.3048 * w

w = 101.2 rad/s = 966.4 rpm

the angular speed of the wheel is 966.4 rpm

b)

at w = 590 rom

w = 590 * 2pi/60 = 61.8 rad/s

speed , v = 61.8 * 0.3048

v = 18.8 m/s = 42.1 mph

the speed of the car is 42.1 mph

c)

as the radius , r = 9/12 = 0.75 feet

reading on speedometer = 48 * 0.75/1

reading on speedometer = 36 mph

the reading on speedometer is 36 mph

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