Mass moment of inertia of an Annulus

Calculates the mass moment of inertia of an annulus or a disk with a hole.
`I_z = 1/2*m*(R^2+r^2)` (about central axis)
`I_x=I_y = 1/4*m*(R^2+r^2)` (about diameter)
Enter 'x' in the field to be calculated.

Rotation axis

Moment of inertia (I)

Mass (m)

Outer radius (R)

Inner radius (r)

Result format

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We use the following formulas to calculate the mass moment of inertia of an annulus (or disk with a hole) that has concentric outer and inner circles.

Case of a rotation about the disc central axis (z-axis on above diagram),
`I_z = 1/2*m * (R^2+r^2)`

Case of a rotation about a disc diameter (x-axis or y-axis on above diagram),
`I_x = I_y = 1/4*m * (R^2+r^2)`

m : mass of the annulus (kg)
R : annulus outer radius in meter (m)
r : annulus inner radius (or hole radius) in meter (m)

Mass moment of inertia of an Annulus

See also