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

Question

At time t = 0 a grinding wheel has an angular velocity of 27.0 rad/s. It has a constant angular acceleration of 35.0 rad/s^2 until a circuit breaker trips at time t = 1.70 s. From then on, the wheel turns through an angle of 440 rad as it coasts to a stop at constant angular deceleration. Through what total angle did the wheel turn between t = 0 and the time it stopped? Express your answer in radians. At what lime does the wheel stop? Express your answer in seconds. What was the wheel's angular acceleration as it slowed down? Express your answer in radians per second per second.

Explanation / Answer

a)At t = 1.70 angular velocity = 27 + 1.70*35 = 86.5 rad/s
From t = 0 to t = 1.7 angle = 1.70*(27+86.5)/2 = 96.475 radians
From t = 1.7 to stopping is 440 radians
so total movement is 96.475 + 440 = 536.475 radians
b) 0^2 - 86.5^2 = 2*a*440
a = -8.50 rad/s^2
t = -86.5/-8.50 = 10.2s
time from time 0 = 1.7 + 10.2 = 11.9 s
c) -8.50 rad/s^2

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