Question

derive the expression for momentum of inertia of a uniform disc about an axis passing through the centre and perpendicular to its plane.​

Answer 1

I=1/2MR²

Explanation:

dI=(dm)r²

as the mass is uniformly distributed, the mass per unit area sigma =mas/ area=M/πR²

dm=¶2πdr=M/πR²(2πrdr)

dI=2M/R²r³dr ,then

I=integration of dI we getas the final answer as( l=1/2MR²)