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## Homework Statement

I'm involved in a dispute about conical pendulums, and my friend, for whatever reason, doesn't want to believe me until somebody backs me up. Assume t is the angle that the string makes with the horizontal.

## Homework Equations

F=ma

## The Attempt at a Solution

Tsint = mg

Tcost = mw^2*r = mw^2*Lcos(t)

T=mw^2*L, where L is the length of the string

Dividing gives:

sin t = g/(w^2*L)

This implies that if w^2*L is smaller than the acceleration of gravity, a conical pendulum cannot maintain a constant angle t with the horizontal.

P.S. this is actually not a homework question. I'm almost certain my calculations are right, but my friend insists that there's no minimum rotation speed for a conical pendulum.