A component of this quantity is given by the derivative of the Lagrangian with respect to angle of rotation about the corresponding axis.
The decomposition of spherical tensor operators acting on the eigenbasis of this operator is the usual application of the Wigner-Eckart theorem. Like spin, the commutator of two distinct components of this operator is given by plus or minus i h-bar times the third component. When transforming between coupled and uncoupled bases for this operator, the (*) Clebsch-Gordan coefficients arise. A component of this quantity is given by the derivative of the Lagrangian with respect to angle of rotation about the corresponding axis. Thus this quantity is conserved in rotationally-invariant systems with no external torque. For 10 points, name this quantity given by displacement cross momentum.
The decomposition of spherical tensor operators acting on the eigenbasis of this operator is the usual application of the Wigner-Eckart theorem.
angular momentum [or orbital angular momentum; prompt on momentum, but do not accept "linear momentum"]