Ablock rests on a wedge on a horizontal surface. the coefficient of friction of the block on the wedge is μ. gravity is directed down. the wedge angle θ obeys tan θ < μ. the wedge is accelerated horizontally at rate a. find the maximum and minimum values of a for the block to stay fixed on the plane.

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.