Moment of Inertia Calculator
Calculate moment of inertia for common shapes including solid sphere, hollow sphere, solid cylinder, and thin rod.
Moment of Inertia
0.080000 kg·m²
Moment of Inertia vs Mass
Fórmula
## Moment of Inertia Moment of inertia (I) is the rotational analogue of mass. It depends on mass distribution relative to the rotation axis. ### Formulas by Shape - **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
Ejemplo Resuelto
A solid sphere of mass 5 kg and radius 0.2 m.
- 01For a solid sphere: I = (2/5) * m * r²
- 02I = 0.4 * 5 * 0.04
- 03I = 0.4 * 0.2
- 04I = 0.08 kg·m²
Preguntas Frecuentes
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.
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