You\'re waiting for your laundry to finish a cycle in the washing machine. You h

Question

You're waiting for your laundry to finish a cycle in the washing machine. You hear it go into the spin cycle, quickly spinning up from rest to an angular speed of 8.0 rev/s in 6.5 s. It spins at that speed for another 5.4 s until you remember that you left your phone in a pocket of the pants you are currently washing. You open the lid, and the tub quickly comes to rest in another 2.5 s. How many revolutions (rev) did the tub go through from the time you heard it start the spin cycle until you saw it stop? Assume constant angular acceleration while it is starting and stopping.

Explanation / Answer

For phage 1: initial angular velocity i  = 0; final angular velocity f  = 8 rev/s and time taken t = 6.5 s

So the angular acceleration = (8 - 0)/6.5 = 1.231 rev/s2  

Now applying second equation of motion (angular counterpart) we get:

total revolutions R1  = 0 + 0.5**t2  = 0.5*1.231*(6.5)2  = 26 revolution

Phage 2: constant = 8 rev/s and time taken t = 5.4 s

Hence total revolutions R2  = *t = 8*5.4 = 43.2 revolution

Phage 3:   i = 8 rev/s ;   f  = 0;   time taken t = 2.5 s

So angular deceleration = 8/2.5 = 3.2 rev/s2

Hence total rrevolutions R3  = 0 + 0.5**t2  = 0.5*3.2*(2.5)2  = 10 revolution

Therefore total number of revolutions in the three phages combined is   

R = R1 + R2 + R3  = 26 + 43.2 + 10 = 79.2 revolutions

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