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The 1st mass moment of a particle is defined as the product of its mass and position vector (Figure 1):
where q = the first mass moment, m = the mass, and r = the position vector. The total mass moment of the system of particles shown in Figure 2 is then
where i = point number.
Center of mass is an imaginary point which suffices the following relationship:
where mtotal = the mass of the system, rCM = the position vector of the CM. In other words, the CM is a single point which effectively represents the whole system. From [3]:
Based on Figure 3, [2] can be rewritten as
The second term of [5] is the total 1st mass moment of the system with respect to its CM. From [3] and [5]:
In other words, the sum of the 1st mass moments of the particles with respect to their CM always becomes zero. |
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© Young-Hoo Kwon, 1998- |
Figure
1
[1]
Figure
2
[2]
[3]
[4]
Figure
3
[5]
[6]