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。

Combination Physical Pendulum

组合物理单摆

A physical pendulum composed of a uniform rod with a sphere on the end of it is an interesting example of a combination pendulum. By examining its moment of inertia, the period is determined to be

一个由均匀杆和一端连接球体组成的物理摆是一个有趣的组合摆例子。通过考察其转动惯量，其周期被确定为

For a rod of length L = cm
and mass mr = gm
attached to a sphere of radius R=cm
and mass ms = gm, with an acceleration of gravity g=m/s2,
the period is T = s compared to a period of s for a simple pendulum for which length equals the distance to the center of mass of the sphere.

对于一根长度为 L = cm、质量为 m 的杆，其一端连接到半径为 R = cm、质量为 m 的球体，当重力加速度为 g = m/s² 时，其周期为 T = s，与单摆的周期相比，该单摆的长度等于球体质心到其的距离。
中文译文中的待填/计算数值依次对应：1：L 2：mr 3：R 4：ms 5：g 6：t 7：ts。实际数值以上方原输入框为准。
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Periodic motion concepts
索引 周期性运动概念
 
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