4:15 PM
@Kate there's only one center of gravity, but where its located can vary, depending on the situation
with a barbell I reckon we often assume it to be fairly constant, even though positioning your hands asymetrical is going to effect what forces are into play
For example, if you move one hand closer to the center, the weight on that side will have a larger moment arm and if unbalanced, would make the other side go up. Off course the other hand will prevent it from doing so, but the forces are completely different
Even with dumbbells there is only one center of gravity for your body, which will be higher, because the dumbbells are now part of the system. But you could break it up into smaller parts. In the end its just a model of reality, because else you'd have to start taking muscles, tendons and their insertion points into account and whatnot.
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5:21 PM
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6:38 PM
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8:45 PM
@Kate As soon as you hold a piece of equipment, you can no longer really speak of the center of gravity of that piece of equipment, because its attached to something
If you hold it on one side, its no longer in freefall, but you get a moment arm from the weights on the end to the point where you're holding it
I guess your point is that if you model an arm (perhaps + weight), like this, each segment on its own still has the same center of gravity
The mathematical definition for the center of mass (or barycenter) of a system with N objects (a system of particles), each with mass mi and position ri is:
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