It takes the Earth 24 hours to make a complete rotation around its axis. 33% Part (a) What is the period of rotation of the Earth in seconds? Grade Summary Deductions0 Potential 100 sin cotan) coso asin) atano acotan) sinh0 tan) acoso Attempts remaining per antemp4) detailed vie cosh0 tanhO cotanhO ODegrees O Radians Hint I give up Hints:-% deduction per hint. Hints remaining:- Feedback: dohction per fcedback ▲ 33% Part (b) What is the angular velocity of the Earth in rad/s? 33% Part (c) Given that Earth has a radius of 6.4 x 106 m at its equator, what is the linear velocity at Earth's surface?

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.