At t=0 a grinding wheel has an angular velocity of 27.0 rad/s. It has a constant

Question

At t=0 a grinding wheel has an angular velocity of 27.0 rad/s. It has a constant angular acceleration of 35.0 rad/s2 until a circuit breaker trips at time t = 2.20 s . From then on, it turns through an angle 434 rad as it coasts to a stop at constant angular acceleration.
Part A
Through what total angle did the wheel turn between t=0 and the time it stopped?

=
rad

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Part B
At what time did it stop?

t =
s

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Part C
What was its acceleration as it slowed down?

=
  rad/s2  

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Explanation / Answer

Total angle that wheel turned between t = 0 and t = 2.20 s:
[(27 rad/s + 35 rad/s^2 * (2.20 s))^2 - (27 rad/s)^2]/(2*35 rad/s^2)
= 144.1 rad
Total angle that the wheel turned between time t = 0 and time it stopped:
144.1 rad + 434 rad = 578.1 rad

Part B:
Wheel's angular velocity at t = 2.20 s is 27 rad/s + 35 rad/s^2 * (2.20 s) = 104 rad/s
angular deceleration = -(104 rad/s)^2/(2*434 rad) = -12.46 rad/s^2
So time wheel stopped is -104 rad/s/(-12.46 rad/s^2) = 8.346 seconds
So the wheel stopped 8.346 seconds + 2.20 seconds = 10.546 seconds from when it started.

Part C:
Angular acceleration = -12.46 rad/s^2

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