Say I have a shelf anchored to the wall (how it's anchored doesn't matter here I think), with a mass (m) taking up most of the space on the shelf:
Say the shelf is x meters long, and the mass is y meters long, such that
y < x, and
(x - y) << x. The mass is pushed right up to the edge of the shelf. Assume the shelf itself is weightless, and that it won't break away from the wall, fracture, or move in any way.
Question: How do I figure out the torque exerted on point A, where the shelf meets the wall?
I know I used to know how to do this, but there's enough missing from my previous knowledge that I can't figure it out and I can't form a good enough search query to find more information.
I know I could find the torque on A if the mass was skinny enough that the distance y was trivial, it would be
m * x. Given that y is not trivial, my brain tells me there should be an integral involved, but I can't figure out what it should be.