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25 January, 04:38

A painted tooth on a spinning gear has angular acceleration α = (20-t) rad/s2, where t is in s. Its initial angular velocity, at t = 0 s, is 320 rpm.

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  1. 25 January, 05:51
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    I think the question will be to find the angular speed at any time t

    Since we are given the initial conditions of the angular speed

    Explanation:

    Given that,

    α = (20-t) rad/s2

    Give the initial condition

    At t=0 w=320rpm

    So modeling a differential equation

    α=dw/dt

    Therefore

    dw/dt = (20-t)

    Applying variable separation

    dw = (20-t) dt

    Integrate Both sides

    ∫dw=∫ (20-t) dt

    w = 20t-t²/2 + C

    C is constant of integration

    Using initial conditions

    At t=0 w=320rpm

    320=0-0+C

    C=320rpm

    Therefore the equation becomes

    W=20t - t²/2 + 320

    This is the model angular speed at any time t
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