1. Consider the diatomic nitrogen molecule N2, which is rotating in the xy plane about the z axis passing through its center, perpendicular to its length. The mass of each nitrogen atom is about m= 2.40×10-26 kg, and at room temperature, the separation between the two-nitrogen atom is d = 1.32×10-10 m. A typical speed of a molecule is 4.60×1012 rad/s. If the nitrogen molecule is rotating with this angular speed about the z axis, what is its rotational kinetic energy? Show your calculation in detail. (Ans: K=2.21x10-22 J)
2. A puck on a frictionless air hockey table has a mass of 5.0×10-3 kg and is attached to a cord passing through a hole in the surface as in the figure shown. The puck is revolving at a distance 2.0 m from the hole with an angular velocity of 3.0 rad/s. The cord is then pulled from below, shortening the radius to 1.0 m. What is the new angular velocity? Show your calculation in detail. (Ans: 12 rad/s)
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