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  • Moment of inertia of a disc about the tangent parallel to the plane is I. What will be the moment of inertia about the tangent perpendicular to its plane ?

Moment of inertia of a disc about the tangent parallel to the plane is I. What will be the moment of inertia about the tangent perpendicular to its plane will be?

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\\\text{The moment of inertia of the disc about an axis parallel to its plane is } \\ I_{t}=I_{d}+M R^{2}$ \\ $\Rightarrow I=\frac{1}{4} M R^{2}+M R^{2}$ \\ $=\frac{5}{4} M R^{2}$ \\ or $M R^{2}=\frac{4 I}{5}$ \\ Now, moment of inertia about a tangent perpendicular to its plane is \\$I^{\prime}=\frac{3}{2} M R^{2}=\frac{3}{2} \times \frac{4}{5} I$ \\\\ $=\frac{6}{5} I$

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