exam2.pdf - Exam 2 PHY 5200 1 A point mass m slides without...

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Exam 2, PHY 5200, 11/11/2016 1. A point mass m slides without friction along a surface z = α ( x 2 + y 2 ), ( α = const > 0), with z axis pointing vertically. The free fall acceleration is g = - g ˆ z . a) How many degrees of freedom the system has? Identify generalized coordinates. b) Write the Lagrangian and the equations of motion. c) Show that M z , the z component of the angular momentum, is conserved.
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