Frictional forces

Can somebody help me in determine the direction of frictional forces at $A,B,C$?

This is my reasoning. If friction was not present due to the weight, the rod AB will fall down and hence the point A should move to the right. Hence $F_a$ is to the left. By resolution of horizontal force, $F_c$ is towards right. By taking moments at O for the sphere, $F_b$ should be downwards. These are wrong.

• What are your thoughts? (Also, this question, although mathematical in some regards, is better suited for Physics Stack) May 31 '17 at 2:16
• Please see the edit. May 31 '17 at 2:19
• Your reasoning and results for $F_a$ and $F_c$ seem correct to me. However, I would suspect that $F_b$ points upwards, as the rod wants to fall downwards under gravity, and friction (due to contact with the sphere), keeps it up. Again, though, this question is better asked on Physics Stack. May 31 '17 at 2:25
• Yes, the main problem that arises in the question is due to $F_b$. How can you justify $F_c$ and $F_b$ by taking moments for the sphere at $O$? Wouldn't they both give a resultant moment? May 31 '17 at 2:26
• Make sure you're talking about the correct force of friction. The force of friction from the rod on the sphere is downward. The force of friction from the sphere on the rod is upwards. May 31 '17 at 2:33