Moment of Inertia - Ellipsoid (axis_1 or axis_2)

The Moment of Inertia of an Ellipsoid rotating about the Axis_{1 or 2} calculator computes moment of inertia about axis₁ or axis₂, the  (the shorter axes, b or c, in the picture) based on the mass, the length of a and b.

INSTRUCTIONS: Choose units and enter the following:

• (m) Mass of the ellipsoid
• (b) Length of axis₂
• (a) Length of axis₃

Moment of Inertia (I₁ or I₂): The calculator returns the moment of inertia in kilograms per square meters. 

Ellipsoid Calculators

• Compute the Moment of Inertia of an Ellipsoid (Axis 3)
• Compute the Moment of Inertia of an Ellipsoid (Axis 1 or 2)
• Compute the Mass of an Ellipsoid
• Compute the Volume of an Ellipsoid
• Compute the Surface Area of an Ellipsoid

The Math / Science

The ellipsoid is defined by the lengths of its three Cartesian axes, where as described in the diagram, `b = c` and `a` lies along the `"axis"_3`.  The Moments of Inertia define the spin of an ellipsoid and have a real world example in the motion of a football. ¹  The formula for the moment of inertia of an ellipsoid around axis 3 is:

`I_1 = I_2 = (m*b^2)/5  * (1 + a^2/b^2)`

where:

• I₁ and I₂ are the moments of inertia of an ellipsoid around axis 1 or 2/
• m is the mass of the ellipsoid
• a is the length of the axis.
• b is the length of the axis.

1. ^ On the Flight of the American Football