Rotational Inertia

hoop about central axis

I= MR^2

Angular cylinder (or ring) about central axis

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

solid cylinder (or disc) about a central axis

I= (1/2)MR^2

solid cylinder or disk about a central diameter

I= (1/4)MR^2 + (1/12)ML^2 (L= length of cylinder)

thin rod about axis through center perpendicular to length

I = (1/12)ML^2

solid sphere about any diameter

I= (2/5)MR^2

thin spherical shell about any diameter

I= (2/3)MR^2

hoop about any diameter

I= (1/2)MR^2

slab about perpendicular axis through center

I= (1/12)M(a^2 + b^2) (a and b are side lengths of slab)