You are helping to design a new fire escape for your third-floor apartment. You step out the window onto a crossbar that is attached to a rope, which in turn is wound around a massive solid cylindrical flywheel that can turn on its axis.
As you fall at increasing speed, the rope causes the flywheel to turn at increasing angular velocity. Your task is to
choose a flywheel that will enable you to move at a safe 2.0 m/s when you reach 10 m below your starting position.
Your mass is 80 kg. Determine the rotational inertia and mass of the uniform 0.80 m radius flywheel you need to
buy.

A( developed during the process of technology design

You throw a baseball directly upward at time =0 at an initial speed of 14.9 m/s. what is the maximum height the ball reaches above where it leaves your hand? ignore air resistance and take =9.80 m/s2.

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.