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 = 2.30s. 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?
At what time does the wheel stop?
What was the wheel's angular acceleration as it slowed down?
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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