First slide

Moment of intertia

Question

For the same total mass which of the following will have the largest moment of inertia about an axis passing through the centre of mass and perpendicular to the plane of the body?

Easy

A

A disc of radius a
B

A ring of radius a
C

A square lamina of side 2a
D

Four rods forming a square of side 2a

Solution

disc = $\frac{m a^{2}}{2}$ , ring=ma²,square lamina= {m(2a)²}/6 four rods making a square of side 2a $[\frac{m}{4} {(\frac{2 a}{12})}^{2} + \frac{m}{4} a^{2}] \times 4 = \frac{37}{36} m a^{2}$

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