Physics - Rotation Question with Solution | TestHub

Moment of inertia of a disc about its own axis (perpendicular to its plane and passing through the center) is $I=\frac{1}{2}M{R}^2$.

By the perpendicular axis theorem, the moment of inertia about a diametric axis is $I_d=\frac{I}{2}=\frac{1}{4}M{R}^2$.

By the parallel axis theorem, the moment of inertia about a tangential axis in its plane is $I_t=I_d+M{R}^2$.

Substituting $I_d=\frac{1}{4}M{R}^2$, we get $I_t=\frac{1}{4}M{R}^2+M{R}^2=\frac{5}{4}M{R}^2$.

Since $M{R}^2=2I$, we have $I_t=\frac{5}{4}(2I)=\frac{5I}{2}$.

Answer: $\frac{5I}{2}$