The tub of a washer goes into its spin cycle, starting from rest and gainiing angular speed steadily for 8.0 s when it is turning at 5.0 rev/s. At this time the person doing the laundry opens the lid and a safety switch turns off the washer. The tub smoothly slows to rest in 12.0 s. Through how many revolutions does the tub turn whil it is in motion.

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Mathematics

9 December, 09:15

The tub of a washer goes into its spin cycle, starting from rest and gainiing angular speed steadily for 8.0 s when it is turning at 5.0 rev/s. At this time the person doing the laundry opens the lid and a safety switch turns off the washer. The tub smoothly slows to rest in 12.0 s. Through how many revolutions does the tub turn whil it is in motion.

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Coralie · Answer 1

Angular acceleration is change of angular velocity over time:

α = 5 / 8 = 0.625 rev / s²

Number of revolutions of the 1st part:

α · t² / 2 = 0.625 * 8² / 2 = 20 rev.

The 2nd part:

α = 5/12 = 0.41667 rev/s²

5 * 12 - (0.41667 * 12² / 2) = 60 - 30 = 30 rev.

In total: 20 + 30 = 50 revolutions