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I'm learning about torques and got really stuck. I hope someone can take the time and help me out with this

When calculating the torque caused by the weight of an object, no matter where we put the axis of rotation, the magnitude of torque m*g*X is always as if the whole mass of a body is pulling from center of mass. I simply can not figure out why that is

Even if looking at formula

m*g*X=(x1*m1+x2*m2 ... )*g

I get no clues what so ever

I know that we can treat extended objects as if the whole body mass was concentrated at that point(center of mass), but ...

Something just doesn't add up

I will give an example

If we have two balls m1 and m2 (m2 > m1) connected together with a stick with length L (its weight is neglible), we find center of that object's mass with

r - is a distance of ball with mass m1 from center of mass

r*m1*g = (l - r)*m2*g

This sounds reasonable

But we could also find center of mass if we don't put rotation axis on center of mass but instead anywhere else. In that case center of mass would be a point where

X*m*g = x1*m1*g + x2*m2*g

This I don't understand! I understand that sum of M1 and M2 would cause the same effect as both those torques together, but why this also gives us a center of mass?

thank you

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# Homework Help: I'm stuck.Really,really need help

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