# Intuitive explanation of moments as they relate to center of mass

I would appreciate it if someone could give me an intuitive explanation of moments. I understand that that the center of mass could be thought of as the point which an object would balance on a fulcrum. But how do moments relate to this idea? My calculus book connects the ideas with equations and formulas, but I can't seem to get an intuition of what is actually happening. If someone could offer up a useful way of thinking of moments it would be most helpful.

Thanks.

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## migrated from math.stackexchange.comOct 23 '11 at 15:45

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It's a physics concept. Did you check out Wikipedia? –  Arturo Magidin Oct 23 '11 at 4:37
You have to see physical density as analogous to probability density, then center of mass is the first moment. –  anon Oct 23 '11 at 4:38
My impression is that migrating a question with an accepted answer is somewhat discouraged, but I think it is clear enough that this should be on physics.SE, so I will migrate. –  Zev Chonoles Oct 23 '11 at 15:44

A moment is the twist as a result of a force at a distance. Go try to loosed the lug nuts of a tire and you will notice that the further away you can push on the wrench, the less effort is needed for the same amount of twisting force.

A simpler example is to try to open a (unlocked & unlatched) door by pushing on it a various distances from the hinge. Try it, and let us know if that gave you a more intuitive feel for moments.

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This was just what I needed. Thank you. –  rkMathUser Oct 23 '11 at 4:56
On a teeter-totter (seesaw) the fat kid has to sit nearer to the fulcrum than the skinny kid if the thing is to balance. The moment due to a kid is his/her distance from the fulcrum, times the kid's weight in the Physics sense (mass times acceleration due to gravity). –  André Nicolas Oct 23 '11 at 5:08

Consider a solid ball of metal weighing one kg. It's center of mass is at its center. If you place it on a table, it weighs one kg, and if you spin it, it's easy to spin, because it's small.

Now take that same ball of metal, melt it down, and concentrate nearly all its mass in a ring like a bicycle wheel (with a little point in the center so you can spin it). Now it still weighs one kg, and its center of mass is still at its center, but it's much harder to spin, because it has a much higher angular moment of inertia, compared to the original ball.

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