Question

In a laundromat, during the spin-dry cycle of a washer, the rotating tub goes from rest to its maximum angular speed of 6.7 rev/s in 8.8 s. You lift the lid of the washer and notice that the tub decelerates and comes to a stop in 16.5 s. Assuming that the tub rotates with constant angular acceleration while it is starting and stopping, determine the total number of revolutions undergone by the tub during this entire time interval.

Answer 1

Answer: 7.095 rev

Explanation: since the motion of the washer is of a constant angular acceleration, then Newton's laws of motion applies.

Recall that

ω = ω0 + αt

Where α = angular acceleration = ?

ω = final angular velocity = 6.7rev/s

ω0 = initial angular velocity = 0 rev/s

t = time taken =8.8s

Since the motion of the dryer starts from rest, ω0 = 0, we have that

ω = αt

6.7 = α(8.8)

α = 6.7/8.8

α = 0.76 rev/s²

This value α = 0.76 rev/s² is a constant value and it is the same all through the motion.

When the lid of the washer was lifted, the motion was of a constant deceleration.

Recall that

θ = ω0t + αt²/2

Where θ = angular displacement

Since the washer is now decelerating, the final velocity (ω= 6.7 rev/s) of the accelerating motion now because the initial velocity of the decelerating motion.

Hence ω0 = 6.7 rev/s, α = - 0.76 rev/s² ( negative sign to denote deceleration) and t = 16.5s

By slotting in the parameters into the formulae, we have that

θ = 6.7 (16.5) + (-0.76)(16.5)²/2

θ = 110.55 - 103.455

θ = 7.095 rev