How to Find the Moment of Inertia of a Cone

Integral calculus produces the formula for a cone's rotational inertia.

A rotating object's moment of inertia describes its resistance to any change in angular motion. The body's mass, which defines its general inertia, factors into this value, but the positioning of the mass around the rotational axis also matters. Divers, for instance, reduce their moment of inertia by tucking in their legs, making their mass more compact. Each shape has its own formula for calculating the moment of inertia; a cone's involves the solid's radius and mass.

Instructions

1. Square the cone's radius. If the radius measures, for instance, 0.3 meters, then 0.3^2 = 0.09.

2. Multiply the result by the cone's mass. If it has a mass, for instance, of 10kg, 0.09 x 10 = 0.9.

3. Multiply this answer by 0.3, a constant factor; in the example, 0.9 x 0.3 = 0.27. This is the cone's moment of inertia, measured in kilogram-square-meters.

References

• Georgia State University: Moment of Inertia
• University of Nebraska--Lincoln: Mass Moment of Inertia

Resources

• University of Ohio: Rotation
• Gazi University: Engineering Statics