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1 May, 22:32

A rotating door is made from four rectangular sections, as indicated in the drawing. the mass of each section is 86 kg. a person pushes on the outer edge of one section with a force of f = 80 n that is directed perpendicular to the section. determine the magnitude of the door's angular acceleration.

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  1. 1 May, 22:38
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    The moment of inertia about the axis will be given by the formula;

    I0 = (1/3) mh², where m is the mass of a section and h is the distance to outer edge.

    Therefore, with four sections combined the inertia will be;

    4*I0 = (4/3) mh²

    But Tor (M) que applied to the door is

    Torque = F * h

    Therefore,

    M = I0 * x

    x = M/I0 (But M = Fh

    = (Fh) / (4/3 * mh² (simplifying the equation)

    = 3F/4mh

    but F = 80 N, m = 86 kg and i assume the height is 1.2 m

    Therefore;

    = (3*80) / (4*86*1.2)

    = 0.581 rad/s²
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