A flywheel of radius R has a distribution of mass given by m() a b, where , is the distance from the center, a and b are constants, and m() is the mass per unit area as a function of The flywheel has a circular hole in the center with radius r Find an expression for the moment of inertia, defined b...

R 2 I mppdA f f mppp dp R 2 t ...

A flywheel of radius R has a distribution of mass given by m() = a + b,

Question:

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 = ʃ^R_rʃ^2π₀ m(ρ)ρ2ρ dϕ dρ.

Distribution
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