- #1
Oerg
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Homework Statement
Ok, so i was trying to derive the moment of inertia about an axis that runs through the centre of mass of the sphere and i couldn't get the answer of [tex]I_{CM}=\frac{2}{5}MR^2[/tex]
The Attempt at a Solution
The moment of inertia is defined as
[tex] \int r^2dm[/tex]
and since
[tex] dm=\rho \times 4\pi r^2\times dr[/tex]
so
[tex] I_{CM}=\int_{0}^{R}4\rho r^4 \pi dr[/tex]
[tex] I_{CM}=\frac{4\rho\pi R^5}{5}[/tex]
and expanding rho gives
[tex] I_{CM}=\frac{3}{5}R^2M[/tex]
which is not correct.