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.

1. consider the case in which air fills air shocks on a truck trailer. the pressure in the shocks is 2 mpa. the temperature is 300 k. the diameter of the shock piston is 10 cm and the initial length of the cylindrical cavity containing the compressed air is 40 cm. a. the truck is gradually loaded over a period of a day in a static setting. the temperature is held constant for the atmosphere and thus for the gas shock. calculate the compressibility of the air in the shock for this condition when the truck is initially being loaded. b. if the shocks were loaded in a dynamic setting by driving over bumps, what would be the compressibility? state your assumption. c. what is the initial load on the shock if the shock is in an atmospheric 100 kpa? d. if the shock is compressed using the process described in part a, and the air shock compressed air cavity length decreases to 20 cm, what is the additional load applied to the shock?

Ameter stick is pivoted at the 0.50-m line. a 3.0-kg object is hung from the 0.15-m line. where should a 5.0-kg object be hung to achieve equilibrium (the meter stick oriented horizontal and motionless)?

Asolid round steel rod 6.25 mm in diameter and 375 mm long is rigidly bonded to the end of solid square brass rod 25 mm on a side and 300 mm long. the geometric axes of the bare are along the same line. an axial tensile force of 5.4 kn is applied at the extreme ends of the assembly. for steel e = 200 gpa and for brass e = 90 gpa. determine the total elongation for the assembly.