Why does it matter where you take moments, when its a lamina?

Question

I've just been doing moments on laminas for the first time and I think I've missed something crucial.

If I take moments around point X, I get:

Clockwise: 30N with a perpendicular distance of 2m = 60Nm

Anti-clockwise: 10N with a perpendicular distance of 4m = 40Nm

So overall moment is clockwise 20Nm

But then if I take moments around point Y (where the 10N force is acting), I get:

Clockwise: 8N with a perpendicular distance of 4m = 32Nm

Anti-clockwise: 12N with a perpendicular distance of 3m = 36Nm and 30N with a perpendicular distance of 2m = 60m

So overall moment is anticlockwise 64Nm

Why don't I get the same moment at X as I do at Y? What is it about laminas that means moments are different, and which moment is the important one?

Answer 1

There is no reason why the total moments about two different points would be the same. On the other hand, if the system reduces to a couple, i.e. two equal and opposite forces but not on the same line, then the moment of the couple would be the same about any point.

The forces in your diagram are not in equilibrium and do not reduce to a couple.

Answer 2

The principle of moments only applies when the object is in equilibrium. In your case, the moments do not come out to be equal for either point selected to take the moment about, and therefore, the object is not in equilibrium. Hope this helped!