A flywheel of radius R has a distribution of mass given by m() = a + b,
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A flywheel of radius R has a distribution of mass given by
m(ρ) = aρ + b,
where ρ, is the distance from the center, a and b are constants, and m(ρ) is the mass per unit area as a function of ρ. The flywheel has a circular hole in the center with radius r. Find an expression for the moment of inertia, defined by I = ʃʃ (ρ)ρ2 dA = ʃRr ʃ2π0 m(ρ)ρ2ρ dϕ dρ.
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