Calculate the moment of inertia of a rod of mass M, and length l about an axis perpendicular to it passing through one of its ends.

Explanation

For the rod of mass M and length l, `I = Ml^(2)//12`. Using the parallel axes theorem, `I ′ = I + Ma^(2)` with `a = l//2` we get,
`I.=M(l^(2))/(12)+M((l)/(2))^(2)=(Ml^(2))/(3)`
We can check this independently since I is half the moment of inertia of a rod of mass 2M and length 2l about its midpoint,
`I.=2M.(4l^(2))/(12)xx(1)/(2)=(Ml^(2))/(3)`