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 30.0 rad/s It has a constant angular acceleration of 28.0 rad/s^2 until a circuit breaker trips at time t = 2.30 s From then on, the wheel turns through an angle of 436 rad as it coasts to a stop at constant angular deceleration. Through what total angle did the wheel turn between t = 0 and the time it stopped? Express your answer in radians. At what time does the wheel stop? Express your answer in seconds. What was the wheel's angular acceleration as it slowed down? Express your answer in radians per second per second.

Explanation / Answer

v = v° + 1/2 a t^2
v° = 30 rad /s
a = 28rad /s2
t = 2.30s
e = v°t + 1/2 a t^2 = 30 *2.30 + 0.5 *28 * 5.29 = 143.06 rad
v = v° + a t = 30 + 28 *2.30= 94.4 rad /s

total angle did the wheel turn between t=0 and the time it stopped 143.06 + 430 = 573.06 rad

t =430 / vmoy = 430 /0.5*94.4 = 9.11+2.3 = 11.11 s

wheel's angular acceleration as it slowed down

a = d v / d t = 94.4 / 9.11= - 10.36 rad /s2

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