Rotational Inertia Equations

have fun

Rotational inertia for a hoop about a central axis

I=MR²

Rotational inertia for an annular cylinder

I=(1/2)M(R₁² + R₂²)

Rotational inertia for a solid cylinder/disk about a central axis

I=(1/2)MR²

Rotational inertia for a solid cylinder/disk about a central diameter

I=(1/4)MR²+(1/12)ML²

Rotational inertia for a thin rod about an axis through the center perpendicular to length

I=(1/12)ML²

Rotational inertia for a solid sphere about any diameter

I=(2/5)MR²

Rotational inertia for a thin spherical shell about any diameter

I=(2/3)MR²

Rotational inertia for a hoop about any diameter

I=(1/2)MR²

Rotational inertia for a slab about a perpendicular axis to the center

I=(1/12)M(a²+b²)

Parallel Axis Theorem

I = I_com+Mh²