Complete the sentences to describe the postulates of Einstein’s special theory of relativity.

Einstein’s special theory of relativity has two postulates.

The first postulate states that the laws of physics are the

same

in all uniformly moving reference frames.

The second postulate states that the speed of light in a vacuum has the same value for all

observers

, regardless of the state of

motion of the observer or the source of light.

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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.