Using the steps to the scientific method, How would you catch the thief of the peanut butter Crackers? - bit of Story- "Over the weekend, Someone broke into the school's cafeteria and stole the peanut butter crackers, leaving no snack for todays lunch. Marks were left on the outside door which could lead to the capture of the peanut butter cracker thief, Find the thief, and you will also find the peanut butter crackers!"

The center of a long frictionless rod is pivoted at the origin, and the rod is forced to rotate in a vertical plane with constant angular velocity \omega. write down the lagrangian for a bead of mass m threaded on the rod, using r as your generalized coordinate, where r, \phi are the polar coordinates of the bead. (notice that \phi is not an independent variable since it is fixed by the rotation of the rod tobe \phi = \omega * t) solve lagrange's equation for r(t). what happens if the bead is initially at rest at the origin? if it is released from any point ro > 0, show that r(t) eventually grows exponentially. explain your results in terms of the centrifugal force m* \omega ^2 *r.