Problem 5: An electric motor is running at 1800 rev/min. It comes to rest in 20 s. If the angular acceleration is uniform find the number of revolutions made before stopping.
Theory: The problem is of circular motion, hence, equations of circular motion will be used. Number of revolutions refers to the angular displacement, where one revolution is 2π radians.
Initial angular velocity = ωi = 1800/60 = 30 rev s-1 , Final angular velocity= ωf = 0, Time = t =20 s
Find Angular acceleration α and angular displacement θ.
Formulae ωf = ωi + αt θ = ωit + ½ αt2
Use first formula to find angular acceleration. Put the values,
0 = 30 + 20α OR α = – (30/20) = – 1.5 revolutions/s
For angular displacement, use the second equation
θ = 30 × 20 + ½ (-1.5) × 202 = 600 – 300 = 300 revs
(Can you convert this displacement to radians)