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.

Solution

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 = ω_i = 1800/60 = 30 rev s^-1 , Final angular velocity= ω_f = 0, Time = t =20 s

Find       Angular acceleration α and angular displacement θ.

Formulae            ω_f = ω_i + αt                                       θ = ω_it + 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