Bilingual edition: English is preserved and Chinese follows each unit. Terminology uses the confirmed v20260916 glossary; automated semantic review remains traceable.
中英双语版：英文原文完整保留，中文紧随对应单元；术语采用 v20260916 确认表，自动语义审校结果可追溯。

Moment of Inertia: Hoop

转动惯量：环形

The moment of inertia of a hoop or thin hollow cylinder of negligible thickness about its central axis is a straightforward extension of the moment of inertia of a point mass since all of the mass is at the same distance R from the central axis.

一个薄圆环或薄空心圆柱体关于其轴线的转动惯量是点质量转动惯量的直接扩展，因为其所有质量都位于距离轴线相同距离R的位置。
For mass M = kg
and radius R = cm
the moment of inertia is
I = kg m2
For a thin hoop about a diameter in the plane of the hoop, the application of the perpendicular axis theorem gives
I(thin hoop about diameter) = kg m2

Show effect of hoop thickness

展示环形厚度的影响
对于质量 M = kg 和半径 R = cm 的物体，其转动惯量为 I = kg m²。对于薄环关于其所在平面内的直径轴，应用垂直轴定理可得 I（薄环关于直径）= kg m²。
中文译文中的待填/计算数值依次对应：1：m 2：R 3：i 4：itd。实际数值以上方原输入框为准。
 Index

Moment of inertia concepts
索引 转动惯量概念
 
HyperPhysics***** Mechanics
力学
R Nave
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Thick Hoops and Hollow Cylinders

厚环与空心圆柱



 For mass M = kg,
internal radius a = cm
and external radius b = cm,
the moment of inertia I = kg m2.
This may be compared with a solid cylinder of equal mass where I(solid) = kg m2, or with a thin hoop or thin-walled cylinder where I(thin) = kg m2.
The moment of inertia of a hollow circular cylinder of any length is given by the expression shown.

Show hollow cylinder development

展示空心圆柱的展开图
对于质量 M = kg，内半径 a = cm 和外半径 b = cm，转动惯量 I = kg m²。这可以与质量相同的实心圆柱体进行比较，其中实心圆柱的转动惯量 I(solid) = kg m²，或与薄环或薄壁圆柱进行比较，其中薄环的转动惯量 I(thin) = kg m²。任何长度的空心圆柱的转动惯量由所示表达式给出。
中文译文中的待填/计算数值依次对应：1：m2 2：a 3：b 4：i2 5：i3 6：i4。实际数值以上方原输入框为准。
 Index

Moment of inertia concepts
索引 转动惯量概念
 
HyperPhysics***** Mechanics
力学
R Nave
 Go Back
返回