A thin rod of length L and mass M is bent at its midpoint

A thin rod of length L and mass M is bent at its midpoint into two halves so that the angle between them is 90°. The moment of inertia of the bent rod about an axis passing through the bending point and perpendicular to the plane defined by the two halves of the rod is:

Mass of each part = M/2
Length of each part = L/2

Total M.I. = Sum of M.I.s of both parts

=		M					L		²	×	1	+		M					L		²	×	1
		2					2				3			2					2				3

= 2 ×	M	×	L²	×	1	=	ML²
	2		4		3		12