點計centre of mass?

2007-04-26 11:10 pm

係另一個知識+ 入面見到:

將所有點既mass乘以perpendicular distance from one point, say point A
之後再除以total mass
得出的是由A去centre of mass既垂直距離

但我都唔係好明點計, 有冇人可以解釋下(跟example)
麻煩晒!!

回答 (1)

天同

2007-04-27 5:53 am

✔ 最佳答案

Centre of mass means that it is the point that all the masses of a rigid body can be construed as concentrated at that point.
Suppose, for simplicity, an object consists of three individual masses m1, m2 and m3 respectively at distances d1, d2 and d3 from an arbituary point A.
The moment by these three masses about point A is thus,
Moment = (m1)(d1)+(m2)(d2)+(m3)(d3)
From definition of centre of mass, we can imagine that if all masses are concentrated at the position where the centre of mass is, the moment should not be changed, hence
(m1)(d1)+(m2)(d2)+(m3)(d3) = (M)(D) = moment about point A
where D is the distance of the centre of mass from point A and M = m1+m2+m3, is the mass of the object.
This gives, D = [(m1)(d1)+(m2)(d2)+(m3)(d3)]/M

👍 0 👎 0