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Object A has mass mA=7kg and initial momentum pA,i=⟨17,−5,0⟩kg⋅m/s, just before it strikes object B, which has mass mB=11kg. Object B has initial momentum pB,i=⟨4,6,0⟩kg.m/s. After the collision, object A is observed to have final momentum pA,f=⟨13,3,0⟩kg⋅m/s. In the following questions, "initial" refers to values before the collisions, and "final" refers to values after the collision. Consider a system consisting of both objects A and B. Calculate the following quantities: The total final kinetic energy of the system.
A mass m is suspended from a massless string, the other end of which is wrapped several times around a horizontal cylinder of radius R and moment of inertia I, which is free to rotate about a fixed horizontal axle. Using a suitable coordinate, set up the Lagrangian and the Lagrange equation of motion, and find the acceleration of the mass m. [The kinetic energy of the rotating cylinder is 1/2 Iω².]