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Demonstrate that in the case of a thin plate of arbitrary shape there is the following relationship between the moments of inertia: I1 + I2 = I3, where subindices 1, 2, and 3 define three mutually perpendicular axes passing through one point, with axes 1 and 2 lying in the plane of the plate. Using this relationship, find the moment of inertia of a thin uniform round disc of radius R and mass m relative to the axis coinciding with one of its diameters. |
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