2. One end of a long rod is fixed at the origin, and the rod rotates about that point in the horizontalplane with angular frequency w. A bead of mass m is constrained to slide without friction along therod (assume the rod is long enough that you don't have to worry about it sliding off the end). Let rbe the radial position of the bead.(a) Find the Lagrangian and equations of motion of the system.(b) Identify a symmetry of the system and find the corresponding conserved quantity. Verify directlyfrom the equations of motion that it is conserved. Show from the equations of motion that thekinetic energy of the bead is not conserved, and explain why.rmFigure 2: Question 2

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