Why would falling on a mattress feel a lot better than falling on a piece of concrete of the same size (and from the same height)? A. The mattress has less mass. B. The impact force felt on the concrete would be greater. C. The mattress would decrease the person's momentum more slowly. D. The mattress would increase the person's momentum more quickly.

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.