Four point masses each of mass m are kept at the vertices of a square abcd of side l. The moment of inertia
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moment of inertia , I = mr² , where m is mass of particle and r is the separation between particle and axis of rotation.
if you want to find moment of inertia about centre of square. then, each point is separated l/√2 from centre of square { axis of rotation.}
hence, moment of inertia = m(l/√2)² + m(l/√2)² + m(l/√2)² + m(l/√2)²
= ml²/2 + ml²/2 + ml²/2 + ml²/2
= 2ml²
hence moment of inertia about centre of square of is 2ml²
if you want to find moment of inertia about centre of square. then, each point is separated l/√2 from centre of square { axis of rotation.}
hence, moment of inertia = m(l/√2)² + m(l/√2)² + m(l/√2)² + m(l/√2)²
= ml²/2 + ml²/2 + ml²/2 + ml²/2
= 2ml²
hence moment of inertia about centre of square of is 2ml²
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