I'm confused about the direction of the normal contact force acting on a body supported by another body. I have read the following :
If a body is being supported by a surface, the normal force acting on the body is always perpendicular to the surface, irrespective of the tilt of the body. https://physics.stackexchange.com/a/366717/326319
Case 1 : Circular motion of a particle inside a circle in a vertical plane
Reaction force is always directed towards center of circle. This is because of circle properties : line joining particle and center is perpendicular to tangent at particle.
Case 2 : A rod AB rests in equilibrium inside a hemisphere in a vertical plane. Part of the rod is outside the hemisphere.
At B, the reaction force acts towards center. However, reaction force at A is not towards center of circle. Why is this so? The surface supporting the rod is vertical so shouldn't the normal contact force be horizontal ? How are points A and B different?
Case 3 : A rod AB rests in equilibrium inside a sphere in a vertical plane. Whole rod is inside sphere.
Based on case 2, am I right to think that the reaction forces at both A and B act towards center?
Case 4 : A horizontal rod AB rests in equilibrium inside a sphere in a vertical plane. Whole rod is inside sphere.
The reaction forces at A and B are also towards center right?
After doing some research, I found this :
- If either surface is differentiable at the point of contact it has a tangent plane there
- If both surfaces have tangent at the contact point then they are necessarily the same plane, or the bodies would intersect.
- If only one has a tangent plane (as in the picture) , use that.
- If neither has a tangent plane there, the direction of the normal is indeterminate.
I also read this discussion.
So I guess, the normal contact force is always perpendicular to the rod if the rod rests on an edge, except at the tip of the rod. My assumptions for the previous cases seem to be correct.
I also concluded the following for the normal contact force acting on a rod in equilibrium against a wall :
There's friction force as well, but I have excluded it.