Physics Question?

Question

Dario, a prep cook at an Italian restaurant, spins a salad spinner 20.0 times in 5.00 seconds and then stops spinning it. The salad spinner rotates 6.00 more times before it comes to rest. Assume that the spinner slows down with constant angular acceleration.

1. What is the angular acceleration of the salad spinner as it slows down?
Express your answer numerically in degrees per second per second.

Answer 1

angular velocity =
20 times/5 sec = 4 times/sec = (4 X 360)deg/sec = 1440 deg/sec

So it goes from 1440 deg/sec to 0 deg/sec
in 6 spins, or (6 X 360) = 2160 deg

Average velocity for the 6 spins = 1440/6 = 240 deg/sec

So (2160 deg)/(240 deg/sec) = (2160/240) (deg) (sec/deg) = 9 seconds

So it takes 9 seconds for the bowl to spin the last 6 times

Angular acceleration = (-1440 deg/sec)/ (9 sec) = (-160)deg/sec/sec

Answer 2

20 spins is 360*20 degrees

20 spins in 5 sec = w = 1440 deg/sec

Angular distance traveled ø = 6*360º:
ø = (w/2)*t (average angular velocity during accel = w/2, This is because accel is constant, that means velocity decays linearly with time.)

t = ø/(w/2)

t = 6*360/720 = 3 sec

The acceration is from w to 0 in t seconds, and is negative:

-1440º/sec / 3sec = -480º/sec^2