For 10 points, name this quantity, whose rotational form is given by one half times moment of inertia times angular velocity squared, often called energy of motion.
The operator of this quantity is negative Planck's constant squared over two times the mass del squared. In the case of a stable gravitational system, its average value over time according to the virial theorem is equal to negative one half times another quantity. This quantity is represented by a capital T in the formula for the Hamiltonian.  The average value of this quantity per molecule in an ideal gas is three halves kt. It is not conserved in inelastic collisions due to heat dissipation. For 10 points, name this quantity, whose rotational form is given by one half times moment of inertia times angular velocity squared, often called energy of motion.
The operator of this quantity is negative Planck's constant squared over two times the mass del squared.
kinetic energy [do not accept "energy" or "potential energy"; accept energy of motion before mentioned; prompt on "K"]