Physics Rotational Inertia Formulas

Hoop about a central axis

I = MR²

SOLID cylinder or disk about a central axis

I = ½ MR²

Thin ROD about perpendicular center axis

I = 1/12 ML² (L is whole length)

Solid Sphere

I = 2/5 MR²

Hoop about diameter (vertically)

I = ½ MR²

Slab (Rectangle)

I = 1/12 M(a²+b²)

Parallel Axis Theorem

I = Icm + Md², where Icm is the moment of inertia about the center of mass and d is the distance from the axis to the center of mass.