At time t=0 a grinding wheel has an angular velocity of 24.0 rad/s . It has a co

Question

At time t=0 a grinding wheel has an angular velocity of 24.0 rad/s . It has a constant angular acceleration of 35.0 rad/s2 until a circuit breaker trips at time t = 2.10 s . From then on, the wheel turns through an angle of 433 rad as it coasts to a stop at constant angular deceleration.

Part A

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

Part B

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

Part C

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

Explanation / Answer

from t1 =0   to t2 = 2.1 s

theta1 = wo*(t2-t1) + 0.5*alfa*(t2-t1)^2

theta1 = (24*2.1)+(0.5*35*(2.1^2)) = 127.6 rad

theta 2 = 433 rad

total angle = thet1 + theta2 = 560.6 rad <<<----------answer

part(B)

from t2 = 2.1 to t3

angular velocity at time t2 = 2.1

w2 = wo + alfa*t = 24 + 35*2.1 = 97.5 rad/s

theta2 = average velocity * t

thet2 = (w2+w1)*dt/2

433 = 97.5*dt/2

dt = 8.88 s

at time dt = 2.1+8.88 = 10.98 s   <,<<-------answer

part(c)

alfa = (w3-w2)/dt

alfa = 97.5/8.88 = 10.98 rad/s^2

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