The negative sign is due to the moment acting in the clockwise direction (acts on the ball).
The cord lengths are
L_{1} = 6 m
L_{2} = L_{1} - πr
= 6 - π (2/π) = 4 m
Substitute known values, and integrate gives,
-T r 2 = 1(4) v_{2} - 1(6)(10)
-6 ( 2/π ) 2 = 4 v_{2} - 60
v_{2} = 13.09 m/s
It needs to be noted that this problem is a simplification of the real situation. The time, 2 seconds, is only an estimate, and the real time will be a function of the velocity which is not known. Also, the tension is a complex function of the cord length and angular velocity, and will not be constant. This simple looking problem is actually complex and beyond this introduction to angular momentum. |