Consider a uniform square plate of side a and mass m. The moment of inertia of this plate about an axis perpendicular to its plane and passing through one of its corners is

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(1) 2/3ma². About the perpendicular axis through the centre: I_cm=m/(12)(a²+a²)=(ma²)/6. The corner is half a diagonal from the centre: d=(a√2)/2=a/(√2), so d²=(a²)/2. Parallel-axis theorem: I=(ma²)/6+m(a²)/2=(ma²)/6+(3ma²)/6=(4ma²)/6. I=2/3ma².

Consider a uniform square plate of side a and mass m. The moment of inertia of this plate about an axis perpendicular to its plane and passing through one of its corners is

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