Amodel of quantized rotational motion of a diatomic molecule (like o2) is the quantum rotator: two particles of mass m are separated by a massless rod of fixed length 2r. this barbell is free to rotate in 3d about its center of mass, which is fixed in space at r-0. (a) express the classical ke of the rotator in terms of its angular momentum and the moment of inertia. since pe is constant for the rotator (and can be set equal to zero), substitute the quantum operators for the classical quantities to obtain the hamiltonian operator of the rotator in terms of the operator of angular momentum. (b) find the energy spectrum enı and the eigenfunctions ynim of the quantum rotator. (c) find the degeneracy of the energy levels of the rotator.

What happens when a rubber rod is rubbed with a piece of fur?

Two cannon balls weighing 18 kg and 24 kg are chained together and fired horizontally with a velocity of 165 m/s from the top of a 21-m wall. the chain breaks during the flight of the cannonballs and the 18-kg cannonball strikes the ground at t = 1.5 s, at a distance of 240 m from the foot of the wall, and 7 m to the right of the line of fire. determine the position of the other cannonball at that instant. neglect the resistance of the air.

The inside surface of a cylindrical-shaped cave of inner diameter 1.0 m is continuously covered with a very thin layer of water. the cave is very long and it is open on both ends. the water on the cave surface is at a constant temperature of 15.5 °c. the cave is constantly exposed to wind such that 15.5 °c air flows through the cave at 4.5 m/s. the kinematic viscosity of the air is 14.66 x 10-6 m2/s and the molecular diffusion coefficient of water vapor in the air is 0.239 x 10-4 m2/s. because the cave diameter is so large, the flow of wind down the length of the cave, in the x direction, can be treated like it is external flow and the cave surface can be approximated as flat where appropriate. calculate the x value, in a) the transition to turbulent flow occurs at rex meters, where the air flow transitions from laminar to turbulent along the inside surface of the cave b) calculate the x value, in meters, where the bulk steady state concentration of water vapor in the air flowing in the cave is 10% of the saturation concentration. assume the air at the surface of the water layer is 100% saturated with water vapor. assume the wind entering the cave contained no moisture before it entered the cave. take into account the transition from laminar to turbulent flow when solving part b