Problem 4: A motor car is travelling at a speed of 30 ms-1. If the wheel has a diameter of 1.5 m, find its angular speed in rad/s and rev/ s.
Strategy: The linear speed of the wheels of the car is to be converted to its angular speed. Remember, radius is half the diameter.
Given Linear speed = v = 30 ms-1 Radius of the wheel = (1.5/2) = 0.75 m
Required Angular speed = ω (in radians and revolutions) = ?
Now the formula for converting linear speed to angular is
Put the values
Now to convert radians to revolutions, we have 2π radians = 1 revolution
So, in radians, the angular velocity = 6.36 rev/s.