- #1

whozum

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[tex] \int_{-L/2}^{L/2} r^2 \frac{M}{L} dr [/tex]

M/L denotes mass density, this evaluates to [itex] \frac{1}{12}mR^2 [/itex] as we'd expect, but my questoin is, if the rod was not rotating about an axis through its center, but an axis at L/5 from its edge, would the integral directly translate to:

[tex] \int_{-L/5}^{4L/5} r^2 \frac{M}{L} dr [/tex] ?

In which case it would evaluate to

[tex] \frac{M}{3L}\left(\frac{4L}{5}\right)^3 - \left(\frac{-L}{5}\right)^3 [/tex] expanded?