There is a mass at the end of a 0.6 m string, being swung around overhead at constant acceleration of(3/4)pi rad/sec^2. mass is 39.84 G. Tensile strength is 12.4 newtons

need to find how many revolutions there will be before the string breaks, and the time before that happens. What equations do I need?

what do you mean acceleration? Is this tangential acceleration?

velocity= 3/4 PI*r*time
tension=mass*velocity^2/r

from that, solve for time.

Then, how many revolutions?

displacement=3/4 PI*time
solve for displacement in radians, then divide by 2PI to get rev.