A question about mobile structures.?

Question

How to take into calculation the weight of the stick in the mobile?

Answer 1

Divide the weight by the length of the stick to get weight density, ρ. Moment produced by the stick then becomes ρd^2/2, since the center of gravity of a stick with uniform density will be at its midpoint, and the weight is ρ times length. The moment produced by the other end of the stick will be ρ(L - d)^2/2.
W1d + ρd^2/2 = W2(L - d) + ρ(L - d)^2/2
2W1d + ρd^2 = 2W2L - 2W2d + ρL^2 - 2ρLd + ρd^2
2W1d = 2W2L - 2W2d + ρL^2 - 2ρLd
2W1d + 2W2d + 2ρLd = 2W2L + ρL^2
2(W1 + W2 + ρL)d = L(2W2 + ρL)
d = L(2W2 + ρL) / (2(W1 + W2 + ρL)
but ρL is the weight of the stick, call it Ws, so
d = L(2W2 + Ws) / (2(W1 + W2 + Ws).
d being the distance to W1 from the pivot point.

It gets a little more complicated if you don't affix W1 and W2 to the ends of the stick.