Open the simulation in Intro mode, and select both Grid and Bar Graph. What happens to the PEG of your skater as you click and drag her vertically? What affects how much the PEG changes? Increase the mass of your skater and repeat step one. Does this change her gravitational potential energy?
Knowing that the acceleration due to gravity (g) on earth affects an object’s gravitational potential energy,
and taking into account your observations from steps one and two, write an equation for PEG

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.