A0.50-kg mass attached to the end of a string swings in a vertical circle (radius 2.0 m). when the mass is at the highest point on the circle, the speed of the mass is 12 m/s. what is the magnitude of the force of the string on the mass at this position?

Which of the following types of electromagnetic radiation has the longest wavelength? a. infrared light b. visible light c. ultraviolet light d. microwaves

According to the image below, which season is about to begin in the southern hemisphere? a. summer b. autumn c. winter d. spring

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.