A Spinning Grinding Wheel?

Question

At time t=0 a grinding wheel has an angular velocity of 26.0 rad/s. It has a constant angular acceleration of 34.0 rad/s^2 until a circuit breaker trips at time t = 2.30 s. From then on, the wheel turns through an angle of 432 rad as it coasts to a stop at constant angular deceleration

a)Through what total angle did the wheel turn between t=0 and the time it stopped?
Express your answer in radians.

b)At what time does the wheel stop?
Express your answer in seconds.


c)What was the wheel's angular acceleration as it slowed down?
Express your answer in radians per second per second.

Answer 1

From t=0 to t=2.3

ω(2.3)=26+34*2.3
104.2 rad/ sec

θ(2.3)=.5*34*2.3^2
89.93 radians

for t>2.3
432=104.2*t-.5*α*t^2
0=104.2-α*t
solve for α and t

t=2*432/104.2
t=8.29 seconds

α=-12.57 rad/s^2

a) The total displacement of the wheel is
89.93+432
521.93 rad

b) the time is
2.3+8.29 seconds
10.59 sec

c) The angular acceleration as it slowed was
-12.57 rad/s^2

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