Calculateur de Moment d'Inertie Gratuit

Calculez le moment d'inertie pour différentes géométries.

Shape

Masse

Radius (or half-length for rod)

Moment of Inertia

0.080000 kg·m²

Moment of Inertia vs Mass

Formule

Moment of inertia (I) is the rotational analogue of mass. It depends on mass distribution relative to the rotation axis.

Solid Sphere: I = (2/5) * m * r²

Hollow Sphere: I = (2/3) * m * r²

Solid Cylinder/Disk: I = (1/2) * m * r²

Thin Rod (center): I = (1/12) * m * L²

A solid sphere of mass 5 kg and radius 0.2 m.

Why does shape affect moment of inertia?

Moment of inertia depends on how mass is distributed relative to the rotation axis. Mass farther from the axis contributes more.

What is the parallel axis theorem?

I = I_cm + m*d², where I_cm is the moment of inertia about the center of mass and d is the distance to the new parallel axis.

How is moment of inertia used?

It appears in the rotational form of Newton's second law: tau = I * alpha, and in rotational kinetic energy: KE = 0.5 * I * omega².

Apprendre

Calculate torque from force and lever arm.

Find angular acceleration from torque and inertia.

Compute kinetic energy from mass and velocity.