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20 January, 20:36

A bar on a hinge starts from rest and rotates with an angular acceleration α = 12 + 5t, where α is in rad/s2 and t is in seconds. Determine the angle in radians through which the bar turns in the first 4.88 s.

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  1. 20 January, 20:49
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    Ф = 239.73 rad

    Explanation:

    α = 12 + 15*t

    W = ∫α*dt

    = ∫ (12 + 5*t) * dt

    = 12*t + 2.5*t^2

    then:

    Ф = ∫W*dt

    = ∫ (12*t + 2.5*t^2) dt

    = 6*t^2 + 5/6*t^3

    therefore the angle at t = 4.88s is:

    Ф = 6 * (4.88) ^2 + 5/6 * (4.88) ^3

    = 239.73 rad
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