Derive the moment of inertia of a rectangular plate having sides a and b about an axis passing through one end and perpendicular to the plate.

Dear student,

I = integral (r^2) *dm
rho = m/ab
dm = rho*b*dr
therefore, dI = r^2 * rho*b*dr. plugging in rho we get
dI = (r^2 * m *b*dr )/ab

If you integrate this from 0 to a, you get
I = (m*a^2)/3

Using perpendicular axis theorem, Iz = Ix + Iy so
Iz = [m (a^2 + b^2)]/3

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