In static equilibrium for a ladder leaning against the wall it is supposed to rotate about a point. Why we are not assuming it to slide down as in our practical life?
1) when it slids down, the bottom must move also, and can be messy to write down the relation between the two motions
2) Any istantaneous motion of a rigid body in a plane can be described as a rotation around some point (this point go to infinity for rectilinear motion)
3) with the rotation you can write easily the ladder motion