I am stuck with a question regarding a mass attached to a rope of negligible mass. This mass is moving in circular motion. I have calculated the net force in the y direction to be equal to T+Fc-mg= 0 but when I check my answer it says that T-Fc-mg= 0. Why would this be? Isn't tension and centripetal force both pointing towards the centre of centripetal motion.
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It sounds like you have an object that is instantaneously at the bottom of a circle, moving at some known speed, as it hangs from a massless rope of known radius. I assume it is at the bottom of the circle because you have T and mg pointing in opposite directions. It is true that Fc will point upward, so will have the same sign as T. The mistake you are making is a common one-- you are treating Fc as if it was another force, like as though there were 3 forces on the mass. This is not the case, the only forces will be from things touching the mass, or gravity, that's it. The centripetal force is none of those, so it is not something you include as a force on the object, instead, it is what happens to the ma for circular motion. You replace ma with Fc, which means that Fc is the net force, it is what the other forces add up to. So you should say Fc = T - mg, where the + sign of T means it points upward, the - sign of mg means it points downward, and the + sign of Fc just means that you are calculating the net upward force by summing the 2 actual forces acting on the mass. You also know that to move in a circle, you must have Fc = mv^2/r, which again is just what ma becomes for circular motion, and shows that the net force must be positive, i.e., must point upward here. Try the same reasoning when the mass is at the top of the circle, and note that then Fc = -T-mg, and also Fc = -mv^2/r.
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$\begingroup$ Oh! I see! Thank you so much! That makes much more sense and yes, sorry I forgot to explain where the object was but you described it perfectly $\endgroup$ Commented Apr 1, 2017 at 1:31