关于刚体重心的讨论

A Discussion on the Center of Gravity of Rigid Body

设想一个简单刚体 ,它是由长度为的刚性轻杆连接两个质量均为m的质点A和质点B组成。当l不太长 ,整个刚体处于均匀重力场中 ,其重心位于轻杆的中点 ,与质心相重合。如l很长很长 ,以致于质点A与质点B所在处的重力加速度或是大小不相等 ,或是方向不相互平行时 ,其重心将不再与质心重合。刚体在空间取向不同 ,重心位置可能不同。由此说明重心的概念不宜推广到太大的物体。另一方面又通过演算说明有理由认为实际的物体都是处于均匀重力场中 ,也没有必要把重心的概念推广到太大的物体。

A simply rigid body is hypothesized in this paper.It is made up of a ligh rigid rod whose length is 1 and two mass points ,A and B,the mass of which is m respectively.When 1 is not long,the whole rigid body is in the well proportioned field of gravity and the whole body′s center of gravity,as the center of mass,is in the middle ofthe rod.But if 1 is so long that the gravitaional acceleration or the gravity of the mass points A and B are not equivalent,or the directions are not parallel,the center of gravity will depart from the center of mass.If bodies posit in different directions,the positions of center of gravity will be different.For this case,the conception of center of gravity on the body of large size is not appropriate.On the other hand,by calculation.it is reasonable to think that bodies are all in well proportioned field of gravity and that it is not necessary to extend the conception of center of gravity to too large bodies.