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.

When temperature of a substance increases, of its particles increase resulting in more between particles. real world applications of thermal expansion absolute zero (-273 degrees c) is the lowest possible temperature on the kelvin scale. it is a measure of where a substance has no kinetic energy. heat is a process of the . energy flows spontaneously from a object to a until equilibrium is reached. heat is measured in heat is transferred throughis a method of heat transfer that occurs between particles of matter that are in direct contact with each other. are poor conductors that impede / reduce the rate of heat transfer. is a method of heat transfer that occurs in fluids (non-solids) by means of currents. real world application of convectiona method of heat transfer through electromagnetic waves. when energy moves from one object to another inside a closed system, no energy is or in the system in the transaction. systems will spontaneously move to a state of organized energy or high disorder over time called

Earth's atmosphere is composed of mostly two gases. name the two gases that make up the majority of the atmosphere and use the pie chart to tell the percentages of each.

You are driving to the grocery store at 20 m/s. you are 110m from an intersection when the traffic light turns red. assume that your reaction time is 0.50s and that your car brakes with constant acceleration. how far are you from the intersection when you begin to apply the brakes? what acceleration will bring you to rest right at the intersection? how long does it take you to stop after the light changes? the known values: vi=20m/s xi=110m t=.50s vf=0m/s xf=0m a=?