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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.


Solution

$$\displaystyle r_{1}= \left( \frac{m_{2}}{m_{1}+m_{2}}\right) r$$
$$\displaystyle r_{2}= \left( \frac{m_{1}}{m_{1}+m_{2}}\right) r$$
$$ I_{c}=m_{1}r_{1}^{2}+m_{2}r_{2}^{2}$$
$$l=\mu r^{2}$$ where $$\displaystyle \mu =\frac{m_{1}m_{2}}{m_{1}+m_{2}}$$ is called the reduced mass of two masses.
233892_215984_ans_0576cde5a1c34ac6ac74da17cafbc5a4.png

Physics

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