Find the moment of inertia of a uniform semicircular disc of mass M and radius R about an axis perpendicular - Physics - System Of Particles And Rotational Motion

Question

Find the moment of inertia of a uniform semicircular disc of mass M
and radius R about an axis perpendicular to its plane and passing
through point P as shown

Ved Prakash Lakhera · Accepted Answer

Let the mass per unit length of the semicircular disc be M12πR2
Let us take a small strip of area πx dx, so mass of this strip is,   mass of the strip=M12πR2
πx dx
Therefore moment of inertia about the given point P,  I = M12πR2
πx dx
 x2or                                    I = 2MR2∫0Rx3 dx = 2MR2x440R=2MR2×R44=12MR2

Find the moment of inertia of a uniform semicircular disc of mass M and radius R about an axis perpendicular to its plane and passing through point P as shown.