centres of mass and moments (further maths)

hi! i have a question i'll attach below. in the answers it says to take moments about A after finding that the centre of mass is 5/pi cm away from the centre of the semicircle. It says 5X = 5/pi * 0.4g

I get that these are the moments due to force X and the weight respectively, but they are acting perpendicular to one another so I don't get how you can equate these? Can someone explain please :smile:

Reply 1

apolaroidofus

centres of mass.jpg57.3KB

Reply 2

mqb2766

I take it you know the com of the wire arc is displaced to the right of the centre of AB so it will provide a clockwise moment about A. Using
moment = force*perp distance
the perp distance would be to the right of A (at 3 o clock) "some value" and gravity can be thought of acting downwards through it.

The horizontal force at the bottom (at 6 o clock) produces an anticlockwise moment (obvious perp distance) and the two moments must balance.

For rotational moments, theres nothing special about the 3 or 6 o clock. Its all rotations about a point, whatever the angle is.