Margaret is going to Yosemite National Park with her family. She wants to do some hiking, but she is going with some relatives who are n thletic. She has found a service that will drop them all off at the top of one of the hills so that they just have to walk down, which she figu be much easier than walking up. What is the BEST advice for Margaret?​

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.