Find the moment of inertia of ring about an axis passing through the centre and perpendicular to its plane.

Find the moment of inertia of ring about an axis passing through the c

1.	Find the moment of inertia of ring about an axis passing through the centre and perpendicular to its plane.
Answer» SOLUTION :A uniform circular RING of radius R and mass M rotating is fixed AXIS passing through its centre, perpendicular to its plane of rotation with constant angular velocity `omega`. Every mass element of this thing is at a distance R from the centre. Hence it rotates with `Romega` linear speed. KINETIC energy of ring `K=(1)/(2)Mv^(2)` `K=(1)/(2)MR^(2)omega^(2)` Equating this, with equation `K=(1)/(2)Iomega^(2)`, `therefore I=MR^(2)`