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A spinning wheel on a fireworks display is initially rotating in a counterclockwise direction. The wheel has an angular acceleration of -3.80 rad/s2. Because of this acceleration, the angular velocity of the wheel changes from its initial value to a final value of -21.0 rad/s. While this change occurs, the angular displacement of the wheel is zero. (Note the similarity to that of a ball being thrown vertically upward, coming to a momentary halt, and then falling downward to its initial position.) Find the time required for the change in the angular velocity to occur.


    since it ends up at the same spot, it goes one way for the same time and distance that it goes the other way. Therefore find half the time and double it.
    0 = Vo + a t
    so a t = -Vo
    Vo = +21 m/s (by symmetry)
    - 3.8 t = -21
    t = 21/3.8
    we want 2t = 42/3.8

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