Why was Aristarchus’s model not accepted? Check all that apply.

Aristotle had better data than Aristarchus.
Aristarchus was not as famous as Aristotle.
Aristotle’s model was more accurate.
Aristarchus could not answer some important questions about the model.
Aristarchus had fallen out of favor with Alexander the Great

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.