Understanding Center of Mass: Common Misconceptions Explained

[BioGuy]

so I am not too sure how to answer a question... ill word it the best i can:

While doing an experiment where we use a Plumb Line and paper object and find the center of mass by letting the string (with mass attached to other end) hand and draw lines that eventually intersect at on specific point. why is it wrong to say that half the mass is on one side and the other half is on the other?

 

[SeanGillespie]

I don't think it is wrong to say that. It sounds logical to me. In the case of a triangle, the centre of mass is the intersection of the medians. So if you hang the triangle and plumb-line from one corner, the plumb-line will hang directly along the centre of the triangle; this therefore indicates that the mass is even on either side.

If the mass were not even on either side of the triangle then the triangle would pivot until it is at equilibrium.

 

[Doc Al]

why is it wrong to say that half the mass is on one side and the other half is on the other?

The center of mass has to do with how the mass is distributed in space, not merely the amount of mass. In general it's not true that a line passing through the center of mass would divide the mass in half. Example: Imagine a thin stick with a 1 kg mass stuck on one end and a 2 kg mass stuck on the other. Where's the center of mass? Somewhere along the stick, closer to the 2 kg mass. But is the mass equally divided on both sides of the center of mass? No.

(Even for a triangle it's not true, depending on how you draw the line.)

 

[SeanGillespie]

I disagree; If an object is hung from a point, as described, it will come to rest by balancing it's mass evenly towards the centre of the earth. If you were to hang a plumbline on the same point, the plumbline will likewise hang towards the center of the earth. It is the same principle of a pendulum, the mass will accelerate toward its point of balance.

Using a plumbline is by no means accurate, however.

My understanding could be flawed, but as it stands at present I cannot see any other explanation. I would be interested to know why this belief does not stand...

 

[Doc Al]

I disagree; If an object is hung from a point, as described, it will come to rest by balancing it's mass evenly towards the centre of the earth. If you were to hang a plumbline on the same point, the plumbline will likewise hang towards the center of the earth. It is the same principle of a pendulum, the mass will accelerate toward its point of balance.

It's true that if you hang an object so that it's free to rotate about the point of suspension, its center of mass will end up directly beneath the point of suspension. But that does not mean that a vertical line drawn through the point of suspension will divide the mass into equal portions. (It's the torque that has to balance, not the amount of mass.)