Moment of Inertia Derivation
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Last updated 7:45 PM on 3/19/26
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7 Terms
1
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\int_{-\frac{L}{2}}^{\frac{L}{2}}\!\!\rho\pi R^2x^2\,dx
V=\pi R^2x
2
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\int_0^{L}\!\rho\pi R^2x^2\,dx
V=\pi R^2x
3
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\int_0^{a}\!\rho bhx^2\,dx
V=bhx
4
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\int_{R1}^{R2}\!2\rho\pi Lx^3\,dx
V=\pi x^2L
5
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\int_0^{R}\!2\rho\pi Lx^3\,dx
V=\pi x^2L
6
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\int_0^{M}\!r^2\,dm
Let R=r
7
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Use volume of a disk, let r²=R²-z²
Let z be along the axis of rotation
\int_{-R}^{R}\rho\pi\left(R^2-z^2\right)^2dz
V=\pi r^2z
