免费转动惯量计算器
计算不同形状物体的转动惯量。
Moment of Inertia
0.080000 kg·m²
Moment of Inertia vs Mass
公式
## 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
计算示例
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
常见问题
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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