How Does Mass Influence the Velocity of the Center of Mass?

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The discussion centers on the concept of the center of mass (COM) and its velocity, defined by the formula V(C) = (m1*v1 + m2*v2...)/(m1 + m2...). The velocity of the center of mass is heavily influenced by the mass of individual objects within a system, particularly when one object is significantly more massive than others. In scenarios where a very large mass (M1) is present, the velocity of the center of mass (V(C)) approaches the velocity of that large mass (V1), even if V1 is much smaller than the velocities of lighter objects (V2, V3). This highlights the dominance of mass in determining the COM's behavior.

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Center of mass and its speed

hi,I'm not shure if this belongs in math section or here

The center of mass is special point in body and is moving as if whole mass was in it.

Velocity of center of mass V(C)= ( m1*v1 + m2*v2... )/(m1 + m2...)

V(c) is in a way an average speed of all the individual speeds bodies in the system have. Value of V(C) depends most on the mass of individual objects in a system. If system contains one very massive body and several others with small mass, then value of V(c) will be very close to the speed of a body with large mass.


It does make some sense,but I'm looking at formula
V(C)= ( m1*v1 + m2*v2... )/(m1 + m2...) and can't figure out how does that work out in this formula. If M1 has very large mass and speed V1 smaller approx. by factor 100 from speeds of other bodies, why would formula for V(C) give result that is closer to V1 than say to V2 and V3 ?

thank you in advance
 
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It might help to think about it this way: What happens to the center of mass when the mass of the lighter object goes to zero?
 

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