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.

Solution

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.