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MOMENTS OF INERTIA EXAMPLES

MOMENTS OF INERTIA EXAMPLES

In many cases for a uniform body, the total mass m is given instead of the mass density. For a uniform plate, the mass is m = ρV = ρhs2. Using the mass instead of the mass density, the moment of inertia about the x axis is
(6) I = (m)/(12)(h2 + s2)
The same process can be used to obtain Iyy and Izz. The only difference between the inertia properties is r used in 1↑.
(7) Iyy =  ⌠⌡Vρ(xi + zk)⋅(xi + zk)dV =  ⌠⌡Vρ(x2 + z2)dV = (m)/(12)(h2 + s2)
(8) Izz =  ⌠⌡Vρ(xi + yj)⋅(xi + yj)dV =  ⌠⌡Vρ(x2 + y2)dV = (m)/(12)(s2 + s2)
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