Two discs A and B each of radius $r$ and mass $m$ are attached as shown to form a system. The moment of…
Two discs A and B each of radius $r$ and mass $m$ are attached as shown to form a system. The moment of inertia of this system about an axis perpendicular to the plane of the discs and passing through the center of disc $\mathrm{A}$ is
$\frac{9}{2} m r^2$
$m r^2$
$2 m r^2$
$5 m r^2$
Solution
The moment of inertia of the disc about the centroidal axis is $\frac{m r^2}{2}$
The moment of inertia of the disc at A about the axis passing through B is given using the parallel axis theorem as $\frac{m r^2}{2}+m(2 r)^2$
Thus, the total moment of inertia of the whole system is given as $\frac{m r^2}{2}+\frac{m r^2}{2}+m(2 r)^2=5 m r^2$
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