T is tension... he's referring to one of those ferris wheel problems asking what is the force of tension on the carriage while it is at the top/bottom of the revolution... I messed up on my answer because I thought you would get the gist so I didn't worry about the details... Fc=mv^2/r ... now let's say the mass is at the bottom of the revolution like you said, now let's find the net force. The force of tension and the force of gravity are in opposite directions (tension up, towards the center, and gravity down) so you know to subtract... but which to subtract from which... You want the net force to be positive, so if they tell you both forces just put the bigger one first... but let's say you're solving for tension. How do you know if tension is bigger and you should write T-mg=mv^2/r or gravity is bigger and you should write mg-T=mv^2/r.. if you don't know how big tension is... well the way to find out is to look at which direction the centripetal force needs to be pointing... the centripetal net force should always point to the center, so if the mass is at the bottom like we assumed you know that the net centripetal force should be pointing... up... well since the net force must point up (and must be positive), you know that the force of tension must be greater than the force of gravity... thus you use T-mg... that's your answer... using mg-T in this case would give you a) a negative net force or b) a net force pointing away from the center ...thats bad
btw, disregard my post above, if the mass is at the top of the revolution, both the force of gravity and force of tension would be pointing down and the net force would just be T+mg