Rotating System in an Inelastic Collision

[IWuvTeTwis]

Homework Statement

Suppose that in the figure below, script i = 0.88 m, L = 2.2 m, M = 1.2 kg, and m = 0.6 kg. The string breaks when the system's angular speed approaches the critical angular speed ωi, at which time the tension in the string is 108 N. The masses then move radially outward until they undergo perfectly inelastic collisions with the ends of the cylinder. Assume that the inside walls of the cylinder are frictionless. (For clarification, M = 2 multiplied by m and the moment of inertia of the hollow cylinder is ML^2/10. Consider the sliding masses to be point masses.)

Find the critical speed that requires the string to break. Also find the final speed after the inelastic collision.

Homework Equations

Conservation of Angular Momentum: Linitial = Lfinal
L = I*omega

The Attempt at a Solution

Because of the law of conservation of momentum I realize that I can forge a relationship between the angular speed before and after the string breaks. Iinitial*omegainitial = Ifinal*omegafinal

However, what I am unsure of is what force causes the string to break. I don't think its the centripetal force since it pushes inwards. Can it be caused by some torque? I would be welcome any suggestions.

 

[ideasrule]

I think you're not understanding centripetal force. Centripetal force is the force that the string applies to keep the mass moving in a circle. In other words, it's the tension in the string. When the system is rotating too fast, the mass's centripetal acceleration becomes too high. The string tries to supply the necessary force to provide this acceleration, but it isn't strong enough, so it breaks.

 

[IWuvTeTwis]

Ok, I've tried using the equation F = 2*m*r*omega^2 where r = 1/2i. The 2 is there because there are two masses. However, I get an answer of 50.3 1/s^2 which doesn't seem to be right. Am I misapplying the centripetal force? Or is there another force I'm not accounting for?