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    calculation of the moi

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    تاريخ التسجيل : 05/04/2008

    m15 calculation of the moi

    مُساهمة من طرف teacher في الثلاثاء 15 يوليو 2008, 12:49 am










    Calculation of the MOI




    Calculation of the MOI

    In computation of the moment of inertia, one can replace the summation shown in [2] of Inertia Tensor by an integration over the body:
    [1
    where r = the perpendicular distance from the particle to the axis of rotation, and dm = the mass of the particle which is a function of the density.Thin Rod

    Let's now apply [1] to a thin uniform rod shown in Figure 1. The MOI of the rod about the Y axis is
    Figure 1
    [2]
    since
    [3]
    where r = the density of the rod, m = the mass of the rod, and L = the length of the rod.
    Circular Ring

    The moment of inertia of the uniform circular ring shown in Figure 2 about the Z axis (the symmetry axis) is
    Figure 2
    [4]
    since
    [5]
    where dl = the length of the arc formed by dq. [5] is also applicable to a circular cylinder.
    Circular Disc

    A uniform circular disc of radius R can be considered as a cascade of uniform circular rings as shown in Figure 3. Thus, from [5], the moment of inertia about the Z axis (the symmetry axis) becomes
    Figure 3
    [6]
    since
    [7]
    [6] can be used in computing the MOI of a circular bar about its longitudinal axis as well.
    Sphere

    A uniform sphere can be considered as a cascade of uniform circular discs as shown in Figure 4. From [6], the moment of inertia about the vertical axis (Z axis) is
    Figure 4
    [8]
    since
    [9]
    See BSP Equations for the moment-of-inertia equations for the geometric shapes commonly used in the human body modeling

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