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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.