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

Question

At time t=0 a grinding wheel has an angular velocity of 27.0rad/s . It has a constant angular acceleration of 34.0rad/s2 until a circuit breaker trips at time t = 2.00s . From then on, the wheel turns through an angle of 435rad 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

w0 = 27 rad/s

a = 34 rad/s^2

Angular velocity at 2 s = w2 = w0 + a t = 27 + 34*2 = 95 rad/s

Angle , th wheel turned during 2 s = ( (w2)^2 - (w0)^2 ) / 2 a = ( 95^2 - 27^2)/(2*34) = 122 rad

Then wheel rotated for 435 rad until it stops

S = 435 rad

deceleration = d = (w2)^2 / (2*S) = 95^2 / (2*435) = 10.3735 rad/s^2

time taken to stop from 2 s = w2 / d = 95 / 10.3735 = 9.158 s

ttoal time taken to stop = 2 + 9.158 = 11.158 s

total angle rotated = 122 + 435 = 557 rad

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Answer

a) total angle rotated = 557 rad

b)  time does the wheel stop = t = 11.158 s

c)  wheel's angular acceleration as it slowed down = 10.373 rad/s2

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