Fall 2006 2 Mech

A bead of mass m is constrained to move along a rigid, frictionless wire attached to a rotating disk at an angle $\theta \le \frac{\pi}{2}$ to the plane of the disk, and at a radius R from the origin. The wire rotates with the disk with angular velocity $\omega$. At the origin of the disk is a mass M with exerts a gravitational force on m. Ignore the gravitational force of the Earth.

(a) If x is the position of the bead along the wire, write down the Lagrangian function for the bead.

(b) Derive the equation of motion for the bead using Lagrange's equation.

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