What is mass moment of inertia?

Mass moment of inertia J is the rotational analog of mass. It determines resistance to angular acceleration: T = J * alpha.

How to find J for complex rotors?

Break into simple shapes, calculate J for each, use parallel axis theorem: J = Jcm + md^2.

k = sqrt(J/m). Distance where all mass could concentrate to give same J.

Yes, J is proportional to length via mass for cylinders.

KE = 0.5*J*omega^2. Used in flywheel and acceleration calculations.

Free Engineering Tool #073

Calculate mass moment of inertia J for solid cylinder, hollow cylinder, disc, and sphere. Enter dimensions and material density.

Multiple ShapesMaterial DensityAuto-Calc

Moment of Inertia J

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Mass

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Radius of Gyration k

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KE at 1000 RPM

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For complex rotors, sum individual section inertias using parallel axis theorem: J = Σ(J_i + m_ir_i²).