Question

The tub of a washer goes into its spin-dry cycle. It starts from rest and accelerates at an angular acceleration of 32.6 rad/s/s for 8.4 seconds. At this point, the person doing the laundry opens the lid, and a safety switch turns off the washer. The tub slows to rest in 10.7 seconds.How many revolutions did the tub make in the first 8.4 seconds?

Answer 1

Answer: the tub makes approximately 1939.25 revolutions in the first 8.4 seconds before slowing down to rest in the next 10.7 seconds.

Explanation:

the final angular velocity of the tub is:

ω = 32.6 x 8.4 = 274.44 rad/s

During the 8.4 seconds, the tub undergoes angular displacement given by:

θ = (1/2) x α x t^2

where θ is the angular displacement.

thus the angular displacement of the tub is:

θ = (1/2) x 32.6 x (8.4)^2 = 12185.44 rad

The tub makes one full revolution when it completes an angular displacement of 2π radians

N = θ / 2π = 12185.44 / (2 x π) = 1939.25 revolutions (approx)?

is it correct?