Apulley of radius r has a string wrapped around it. a force is applied to the free end of the string such that the string has a tension t. assume that the pulley is rotating with constant angular velocity in the counter-clockwise direction (this could be accomplished by a frictional force which is counteracting the torque due to the string). convince yourself that while the pulley rotates by an angle θ a point on the boundary of the pulley moves by the distance d=rθ. therefore the work done by the tension force on the pulley is given by w=td=trθ.

a. what is the torque τ on the pulley due to the tension in the rope?

b. rewrite the expression for the work done on the pulley by the rope (given above) using your expression for the torque τ. the formula you obtain is the general formula for the work done by a torque on a rotating object. explain why it can be said that this formula is analogous to the formula for work done by a force for linear motion.

Acharge of 8.4x10^-4 c moves at an angle of 35 degrees to a magnetic field that has a field strength of 6.7x10^-3 t. if the magnetic force is 3.5 x10 ^-2 n, how fast is the charge moving?

Velocity is a description of both speed and direction, therefore it - a vector - a force arrow - the same as acceleration - a magnitude

Some material consisting of a collection of microscopic objects is kept at a high temperature. a photon detector capable of detecting photon energies from infrared through ultraviolet observes photons emitted with energies of 0.3 ev, 0.5 ev, 0.8 ev, 2.0ev, 2.5ev, and 2.8ev. these are the only photon energies observed. (a) draw and label a possible energy-level diagram for one of the microscopic objects, which has four bound states. on the diagram, indicate the transitions corresponding to the emitted photons. explain briefly. (b) would a spring–mass model be a good model for these microscopic objects? why or why not? (c) the material is now cooled down to a very low temperature, and the photon detector stops detecting photon emissions. next, a beam of light with a continuous range of energies from infrared through ultraviolet shines on the material, and the photon detector observes the beam of light after it passes through the material. what photon energies in this beam of light are observed to be significantly reduced in intensity (“dark absorption lines”)? explain briefly.