moments of inertia - ap physics c mechanics

1/12 ML²

slender rod, axis through center

1/3 ML²

slender rod, axis through one end

1/12 M(a² + b²)

rectangular plate, axis through center

1/3 Ma²

thin rectangular plate, axis along edge

1/2 M(R1² + R2²)

hollow cylinder, axis through center

1/2 MR²

solid cylinder, axis through center

MR²

thin-walled hollow cylinder, axis through center

2/5 MR²

solid sphere, axis through center

2/3 MR²

thin-walled hollow sphere, axis through center