Question

Your car's wheels are 68.00 cm in diameter and the wheels are spinning at an angular velocity of 109.0 rad/s. How fast is your car moving in kilometers per hour (assume no slippage)?

Answer 1

Assuming that there is no slipping, we know that

v = rw

where v is linear velocity, r is radius and w is angular velocity

We are given diameter, we need to convert this to radius and then convert it to meters.

r = d/2 = 68/2 = 34 cm = 34 / 100 = 0.34 m

so,

v = 0.34 * 109

v = 37.06 m/s

To convert it to km/h, we can multiply it by

v = 37.06 * (3600 / 1000)

v = 133.42 km/h