A Spinning Grinding Wheel At time t =0 a grinding wheel has an angular velocity

Question

A Spinning Grinding Wheel

At time t=0 a grinding wheel has an angular velocity of 29.0 rad/s . It has a constant angular acceleration of 34.0 rad/s2 until a circuit breaker trips at time t = 1.50 s . From then on, the wheel turns through an angle of 430 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 secon

Explanation / Answer

A) at t = 0, w1 = 29 rad/s

Total angular dispalcement = w1*t + 0.5*alfa*t^2 + 430

= 29*1.5 + 0.5*34*1.5^2 + 430

= 511.75 rad

B) at t = 1.5s,

w2 = w1 + alfa*t

= 29 + 34*1.5

= 80 rad/s

let t is the time taken to stop

let alfa' is the angular acceeration during slowinf down.

alfa' = (w3^2 - w2^2)/(2*430)

= (0^2 - 80^2)/(2*430)

= -7.44 rad/s^2

time taken to stop, t = (w3 - w2)/alfa'

= (0 - 80)/(-7.44)

= 10.75 s

so, at t = 1.5 + 10.75 = 12.25 s it stops.

C) alfa' = -7.44 rad/s^2

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