Description
The tub within a washer goes into its spin cycle, starting from rest and reaching an angular speed of 16π rad/s in 7.2 s. At this point, the lid is opened, and a safety switch turns off the washer. The tub slows to rest in 16.7 s. Through how many revolutions does the tub turn? Assume constant angular acceleration while the machine is starting and stopping. Answer in units of rev
Explanation & Answer
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Assuming constant angular acceleration while it is starting and stopping.
SPEED UP
Velocity (vi) = 0 rev/s
Velocity (vf) = 16 rev/s
Time (t) = 7.2s
Δx = 1/2 ( vi + vf ) * Δt
Δx = 1/2 ( 0 + 16 ) * 7.2
Δx = 57.6 rev
SLOW DOWN
Velocity (vi) = 16 rev/s
Velocity (vf) = 0 rev/s
Time (t) = 16.7s
Δx = 1/2 ( vi + vf ) * Δt
Δx = 1/2 ( 0 + 16 ) * 16.7
Δx = 133.6 rev
Total revolutions in 23.9 seconds:=133.6+57.6=191.2rev