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Goldstein Classical Mechanics, 3rd Edition. Chapter 6; exercise 3 Question: A bead of mass m is...

Goldstein Classical Mechanics, 3rd Edition. Chapter 6; exercise 3 Question: A bead of mass m is constrained to move on a hoop of radius R.The hoop rotates with constant angular velocity small omega around a diameter of the hoop,which is a vertical axis (line along which gravity acts). (a) set up the Lagrangian and obtain the equations of motion of the bead. (b) Find the critical angular velocity large/capital omega below which the bottom of the hoop provides a stable equilibrium for the bead. (c) Find the stable equilibrium position for small omega> large/capital omega.

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