So the problem Im dealing with has a corresponding diagram below where a mass is being spun in a circular path (at an increasing angular speed) causing the hanging weight to be lifted through the rope. There is a demonstration here by Prof Julius Miller at the 9 minutes and 6 second mark- https://www.youtube.com/watch?v=z3BSkMj1wLc. I wanted someone to explain why this phenmena occurred. Someone did reply and said that T (horizontal)=Mg where M is the hanging weight. But how can T possibly equal Mg? A horizontal force is not related to a vertical force.
For $m$ to undergo circular motion, a centripetal force is required, which is provided by the tension. However, resulting from Newton's Third Law pairs, this tension will apply a force equal in magnitude on mass $M$.
If you spin $m$ at the right frequency, then the magnitude of the centripetal force provided by the tension force will be equal in magnitude to $Mg$.
Although tension is acting (almost*) horizontally on $m$, the (assumed massless) string is vertically connected to $M$, and tension will thus act along that vertical axis.
*I say almost, because provided that the point of rotation remains fixed, $m$ can never spin perfectly horizontally since a component of the tension force is needed to counteract $mg$.
Tension will always act in the direction the string is pointing: