At time t =0 a grinding wheel has an angular velocity of 29.0 rad/s . It has a c

Question

At time t=0 a grinding wheel has an angular velocity of 29.0 rad/s . It has a constant angular acceleration of 35.0 rad/s2 until a circuit breaker trips at time t = 2.50 s . From then on, the wheel turns through an angle of 440 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

A)initial angular velocity is wi = 29 rad/s

angular accelaration is alpha = 35 rad/s^2

time taken is t = 2.5 sec

Using

theta = (wi*t) +(0.5*alpha*t^2)

theta = (29*2.5)+(0.5*35*2.5^2)

theta = 181 rad

total angle is theta+440 = 181+440 = 621 rad

B)

From t = 0 to t = 2.5 sec

Using Wf = Wi+(alpha*t) = 29+(35*2.5) = 116.5 rad/s

after t = 2.5 sec

initial angular velocity is wi = 116.5 rad/s

final angular velocity is wf = 0 rad/sec

then

Using

Wf = Wi+(alpha*t)

0 = 116.5-(alpha*t)

alpha*t = 116.5

and also using

theta = (wi*t) + (0.5*alpha*t^2)

440 = (116.5*t)- (0.5*alpha*t^2)

440 = (116.5*t)-(0.5*116.5*t)

t = 7.55 rad/sec

so total time taken to stop the wheel from t = 0 is t = 7.55+3.32 sec = 10.87 sec

Part C)

alpha*t = 116.5

alpha = 116.5/7.55 = 15.43 rad/s^2

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