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 27.0rad/s . It has a constant angular acceleration of 30.0rad/s2 until a circuit breaker trips at time t = 2.50s . From then on, the wheel turns through an angle of 440rad as it coasts to a stop at constant angular deceleration.

a.) Through what total angle did the wheel turn between t=0 and the time it stopped? (In radians)

b.) At what time does the wheel stop? (In seconds)

c.) What was the wheel's angular acceleration as it slowed down? (In radians per second)

Explanation / Answer

a) angle turned till t=2.5s

= 27*2.5 + 0.5*30*2.5^2 rad = 161.25 rad.

So, total angle turned = 440 + 161.25 = 601.25 rad.

b) angular velocity at the time of application of brake = 27 + 30*2.5 = 102 rad/s.

So, angular decelaration = 102^2/(2*440) = 11.82 rad/s^2.

So, time taken after application of brake = 102/11.82 = 8.63 s

So, total time = 2.5+8.63 = 11.13 s.

c) As calculated in part b,

angular accelaration = -11.82 rad/s^2.

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