Question

how do you find the maximum velocity of a pendulum at the vertical (straight down) with out breaking the tension of the string?

Answer 1

I'm not sure, but I think it might help us both if I write down what I'm thinking.\[\sum T=m\alpha+mg\]\[\alpha=\frac{\omega^2}{r}\]\[T=\frac{m\omega^2}{r}+mg\]If you ignore acceleration due to gravity then the tension of the string is enough to change the momentum of the ball, which will be the maximum tension. Adding anything else, like gravity, should be enough to break the string.
Thoughts?