Question

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?

Answer 1

Answer:

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