Under what conditions are ketone bodies produced? a. ketone bodies are produced when oxaloacetate is in insufficient supply. b. ketone bodies are produced when lipid metabolism lags behind carbohydrate metabolism. c. ketone bodies are produced when the liver is jaundiced. d. ketone bodies are produced when carbohydrate metabolism lags behind lipid metabolism.

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.