Finding the moment of inertia for common shapes

Slender rod, axis through center

I=(1/12)ML^2

Slender rod, axis through one end

I=(1/3)ML^2

Rectangular plate, axis through center

I=(1/12)M(a²+b²)

Thin rectangular plate, axis along edge

I=(1/3)Ma^2

Hollow cylinder

I=(1/2)M(R1^2 + R2^2)

Solid cylinder

I=(1/2)MR^2

Thin-walled hollow cylinder

I=MR^2

Solid sphere

I=(2/5)MR^2

Thin-walled hollow sphere

I=(2/3)MR^2