I believe the normal force on B is not zero, it is equal to the i-component of the force imparted by rod AB but in the opposite direction. But since B moves vertically along a smooth rod this force should not really affect anything.

If you include the rigid bars holding A and B in the system then you shouldn't have to care about either the normal force or the tension force when solving for omega

How do we find the speed of B after getting the omega at theta=90? Since B is on the same axis as O it wouldn't contribute to the angular momentum I think

Should we assume that particle B has no angular momentum

Can we assume that the normal force on B is equal to 0 since it is only constrained to move vertically?

I believe the normal force on B is not zero, it is equal to the i-component of the force imparted by rod AB but in the opposite direction. But since B moves vertically along a smooth rod this force should not really affect anything.

If you include the rigid bars holding A and B in the system then you shouldn't have to care about either the normal force or the tension force when solving for omega

How do we find the speed of B after getting the omega at theta=90? Since B is on the same axis as O it wouldn't contribute to the angular momentum I think