Question

2. Does the fulcrum contribute any torque to the system? Does the weight of the meter stick contribute and torque to the system? If the fulcrum were shifted past the center of mass of the meter stick, say, to the right, would the fulcrum then exert a torque about a point of contact between it and the meter stick? Would the weight of the meter stick exert a torque about that same point?

Answer 1

Since the fulcrum lies at the center of rotation the torque due to fulcrum is zero. The weight of the rod also acts on the center of mass(center of rotation) so the torque due to weight is zero.

if the fulcrum is shifted to right then still the center of rotation lies at the position of fulcrum so the torque due to fulcrum will be zero. The weight acts at the center of mass and hence there is a distance between the weight force and the center of rotation(fulcrum) so the torque due to weight is not zero.