An automobile wheel rotates at 500 rpm. If the wheel has a diameter of 1 meter, what is the velocity of the automobile? If the wheel is underinflated, its radius is only 0.9 meters. What velocity will the car have?

The velocity of the automobile would be 52.36 m/sec

The new velocity of the automobile would be 47.124 m/s

Explanation:

Part A

given

angular speed = 500 rpm = 500 rev/min x 2πrad/60 secs = 52.36 rad/sec

radius of the wheel r = 1 m

velocity v of the automobile can be obtained with the expression below;

ω = v/r

v = ωr

v = 52.36 rad/sec x 1 m

= 52.36 m/sec

Therefore the velocity of the automobile would be 52.36 m/sec

Part B

if the radius changed to 0.9 m

v = ωr

v = 52.36 rad/sec x 0.9 m

v = 47.124 m/s

Therefore the new velocity of the automobile would be 47.124 m/s