# Direction of tension in a vertical circular motion confusion

Suppose you have a ball attached at the end of a string going in a vertical circular motion. We know that the force generated by the centripetal acceleration in a Free body diagram points toward the center of the circle as the ball is going around in a circle

In this problem the point at the top which the string becomes "slack" intuitively makes sense that tension has to be less than the m*g in order for the ball to be slack(loose) at the top. But from the free body diagram the tension should not be pointing opposite of the balls gravity at the top but should point towards the center as well. So my main confusion is that the direction of tension does not match the direction of the centripetal force generated by the tension.

Which direction does the tension act is it just a matter of perspectives?

The tension, if there is any, comes from the pull of the cord.

The tension force on the ball, if there is any, points toward the center of the circle.

But from the free body diagram the tension should not be pointing opposite of the balls gravity at the top but should point towards the center as well. So my main confusion is that the direction of tension does not match the direction of the centripetal force generated by the tension.

You say the tension acts towards the center of the circle (centripetal) and then say that you are confused as to why the tension is not centripetal.

The tension force points towards the center of the circle the entire time, since tension can only act along the cord which is always a radius of the circle. It isn't a matter of perspective.

If the cord is slack at the top then tension is $$0$$. Which I guess makes your statement that it's less than the weight true, but it's more specific to just say it is $$0$$

The tension is always pointing towards the center of the circle.The string becomes slack at the top if the acceleration due to gravity exceeds the centripetal acceleration. Use this fact and energy conservation to determine your minimum speed.