Question

The moment of inertia of semicircular plate of radius r and mass m about axis aa' in its plane passing through its centre is

Answer 1

consider, the mass of semicircular plate = m

and, the mass of the circular plate M = 2*m

⇒ then moment of inertia of the circular plate I =  M*r²/4

substituting the mass M = 2*m

I =[(2*m)* r²]/4

I = m*r²/2

Now integrating the whole plate for semicircular conditions;

I(plate) = ∫r² 2*dm = 2∫r² dm = 2*I(semicircular plate)

I(plate)= 2*I(semicircular plate)

I(semicircular plate) = m*r²/4