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22 February, 22:08

At time t=0 a grinding wheel has an angular velocity of 26.0 rad/s. It has a constant angular acceleration of 25.0 rad/s^2 until a circuit breaker trips at time t = 2.50 s. From then on, the wheel turns through an angle of 440 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?

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  1. 22 February, 22:16
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    The equations of motions will be applied in this question; except that in this case it will be angular motion instead of linear motion.

    We use the formula

    v = u + at; to determine the final velocity of before the circuit breaker trips.

    v = 26 + 2.5 x 25

    = 88.5 rad/s

    Total angle covered before circuit breaker trips:

    2as = v² - u²

    s = (88.5² - 26²) / 2 (25)

    s = 143.125 rad

    Angle covered before stopping after trip = 440 rad

    Total angle covered from start to finish:

    143.125 + 440

    = 583.125 rad

    Acceleration as wheel stops:

    2as = v² - u²; v = 0

    a = - (88.5²) / 2 (440)

    a = 0.1 rad/s²

    Time to stop:

    v = u + at

    0 = 88.5 - 0.1t

    t = 885 seconds

    Total time: 2.5 + 885

    = 887.5 seconds
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