What is the Second moment of inertia of hoop?

The second moment of inertia, also known as the area moment of inertia, for a thin hoop about its central axis is given by the formula ( I = m r^2 ), where ( m ) is the mass of the hoop and ( r ) is its radius. This moment of inertia quantifies the hoop's resistance to bending or flexural deformation in response to an applied load. In this case, all the mass is concentrated at a distance ( r ) from the axis, leading to the direct relationship with ( r^2 ).