How did Pythagoras combine math and philosophy? A. He was a skilled musician as well as a philosopher.
B. He kept track of the number of new philosophies emerging.
C. He believed that math could be used to explain the entire universe.
D. He thought that numbers were the universal element that made up all things.

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While preforming an experiment involving a reaction between two chemicals the scientist observes that the reaction container has become warm the observation is an example of

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.