Question

Two point masses $m_1$ and $m_2$ are joined by a weightless rod of length $r$. Calculate the moment of inertia of the system about an axis passing through its centre of mass and perpendicular to the rod.

Answer 1

$r_1=\left(\frac{m_2}{m_1+m_2}\right)r$
$r_2=\left(\frac{m_1}{m_1+m_2}\right)r$
$I_c=m_1{r}_1^2+m_2{r}_2^2$
$l=\mu r^2$ where $\mu =\frac{m_1{m}_2}{m_1+m_2}$ is called the reduced mass of two masses.