This is a rock tied to a string spinning vertically.
Here,
$T+mgsin\theta = mv_1^2/r => T = mv_1^2/r-mgsin\theta$
Suppose I give it a velocity $v$ at the bottom.
1) At what angle $\theta$ will the tension become zero?
2) If the velocity ends up $=0$ at $\theta = 0$, then the tension $T = m0^2/2-mg$ which would end up giving tension a negative value. How is this possible?
3) If the velocity at any point ends up zero, does the tension necessarily have to end up equalling zero as well?
Best Answer
It isn't. If you set zero speed $v=0$, then you will no longer have circular motion, and the object will accelerate downwards. A non-zero speed $v$ is a requirement for circular motion to happen, because a radial acceleration towards the center can be present only as such. Otherwise it would be like assuming that the object would continue moving around the center even if you stop pulling in the string which obviously isn't the case.