Question

Problems on moment of inertia when mass is removed

Answer 1

The moment of inertia of disc of mass 9M9Mand radius RR about an axis perpendicular to its plane and passing through its centre O is,

Itotal=12(9M)R2=92MR2.Itotal=12(9M)R2=92MR2.

The mass of removed disc is 9MπR2πR29=M9MπR2πR29=M. The parallel axis theorem gives moment of inertia of the removed disc about axis passing through OO as,

Iremoved=12M(R3)2+Md2=118MR2+M(2R3)2=12MR2.Iremoved=12M(R3)2+Md2=118MR2+M(2R3)2=12MR2.

Using, Itotal=Iremaining+IremovedItotal=Iremaining+Iremoved, we get Iremaining=4MR2Iremaining=4MR

Answer 2

i think when mass is removed there will be no inertia because it is basically caused by mass and is directly propotional to it
hope it helps