Physical Pendulum

物理摆

Hanging objects may be made to oscillate in a manner similar to a simple pendulum. The motion can be described by "Newton's 2nd law for rotation":

悬挂物体可能以类似于单摆的方式 oscillate。这种运动可以用 '牛顿第二定律 for rotation' 来描述：

where the torque is

其中力矩是

and the relevant moment of inertia is that about the point of suspension. The resulting equation of motion is:

以及相关的转动惯量是关于悬挂点的。所得的运动方程为：

for small angles where

对于小角度的情况

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This is identical in form to the equation for the simple pendulum and yields a period:

这与单摆的方程形式相同，得出周期为：

Calculation

计算

Compare to simple pendulum

与单摆比较

Rod pendulum

罗德摆

Circular geometries

圆几何

Combinations

组合

Index

Periodic motion concepts

索引周期性运动概念

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Physical Pendulum Calculation

物理摆计算

The period is not dependent upon the mass, since in standard geometries the moment of inertia is proportional to the mass.

周期不依赖于质量，因为在标准几何中，转动惯量与质量成正比。

For small displacements, the period of the physical pendulum is given by

对于小位移，物理摆的周期由以下公式给出