yoyo physics

eosphorus

this is a problem for which i would appreciate any formula:

i make a looping the loop with the yoyo, it means i throw it horizontally recover it make a loop and thro it horizontally again and so on

the initial speed of the yoyo is 1m/s its mass 1 kg the radius of the arm of the yoyo 1m

what would be the perfect lenght of the string for the tension of the string to reach 0 converting to torque the maximum amount of linear speed of the yoyo (remember it will reach amoment the yoyo will give away more string than its velocity allows to keep tension in the string)

i would appreciate any formula and remember im a newbee into physics