The formula for centripetal force is Fr=mv²/r, and for our purposes, we can set all of that to t+mg, to get the formula mv²/r=t+mg. According to the paragraph in Introductioin/Home, we have numeric data we can substitute into this formula, to solve for v, velocity. After substitution, including 9.8m/s²for gravity, we get the equation 10v²/5=0+10*9.8. (We substituted 0 for t, tension in your arm, because we are looking for the slowest speed here, were your arm isn't folding, but also not being streched.) Now that we have this equation, we can simply use algebra to solve for v. It can be simplified to v²/5=9.8, because the masses cancel out on each side, and the zero can be removed. Multiply by 5 on both sides to get v²=49, and after square rooting each side, we get the solution, v=7 meters per second.