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16 January, 18:26

In a downtown office building you notice each of the four sections of a rotating door has a mass of 85 kg. What is the width of each section of the door if a force of 58 N applied to the outer edge of a section produces an angular acceleration of 0.400 rad/s2?

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  1. 16 January, 19:07
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    width = 1.28 m

    Explanation:

    To do this exercise, you need to apply the following expression:

    T = F * d (1)

    T: torque

    F: Force

    d: distance or width in this case

    But T can be also:

    T = 4Iα (2)

    α: angular acceleration

    And I (moment of innertia) is:

    I = md²/3 (3)

    Then, replacing (2) and (3) in the equation (1) you have:

    4md²α/3 = F * d - --> two d cancel themselves

    Solving for d:

    4mdα/3 = F

    d = 3F/4mα

    Now, let's replace the data in this equation:

    d = 3*58 / 4 * 85 * 0.4

    d = 1.28 m
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