How fast do you need to swing a 190-g ball at the end of a string in a horizontal circle of 0.6-m radius so that the string makes a 30 degree angle relative to the horizontal?

Answer 1

tension - T
inward force = T cos 30
so
T cos 30 = m v^2/.6

downward force = mg = T sin 30 = T/2
T = 2 m g

so
2 m g = m v^2/.6

v^2 = 1.2 g

if you want angular velocity
v = omega r
omega = v/.6

Answer 2

the inward force would be in terms of sine wouldn't it?