moment of inertia - some formulae

physics, kinetics

a ring about an axis passing through its centre to the plane's centre perpendicularly

I = mr²

a ring about any diameter

I = mr²/2

a ring about a tangent in a plane

I = 3mr²/2

a ring about a tangent perpendicular to its plane

I = 2mr²

a disk about an axis passing through its centre perpendicularly to a plane

I = mr²/2

a disk about any diameter

I = mr²/4

a disk about a tangent in a plane

I = 5mr²/4

a disk about a tangent perpendicular to a plane

I = 3mr²/2

a thin uniform rod about an axis passing through the centre and perpendicular to it

I = ml²/12

a rod about an axis perpendicular to it

I = ml²/3

hollow cylinder about an axis

I = mr²

solid cylinder about an axis

I = mr²/2

a solid sphere about its diameter

I = 2mr²/5