The assembly of the light rod and two end masses is at rest when it is struck by the falling wad of putty traveling with speed \(v_{1}\) as shown. The putty adheres to and travels with the right-hand end mass. Determine the angular velocity \(\dot{\theta}_{2}\) of the assembly just after impact. The pivot at \(O\) is frictionless, and all three masses may be assumed to be particles.

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4m 21 m U1 2m