In physics, angular momentum intuitively measures how much the linear momentum is directed around a certain point called the origin; the moment of momentum. Since angular momentum depends upon the origin of choice, one must be careful when discussing angular momentum to specify the origin and not to combine angular momenta about different origins.
The traditional mathematical definition of the angular momentum of a particle about some origin is:
- L = r×p
For many applications where one is only concerned about rotation around one axis, it is sufficient to discard the vector nature of angular momentum, and treat it like a scalar where it is positive when it corresponds to a counter clock-wise rotations, and negative clock-wise. To do this, just take the definition of the cross product and discard the unit vector, so that angular momentum becomes:
- L = |r||p|sinθ
- L = ±|p||rperpendicular|
- L = ±|r||pperpendicular|
The conservation of angular momentum is used extensively in analyzing what is called central force motion. In central force motion, two bodies form an isolated system not influenced by outside forces, and the origin is placed somewhere on the line between the two bodies. Since any force the bodies exert on each other must be directed along this line, there can be no net torque, with respect to the afore-mentioned origin, on either body. Thus, angular momentum is conserved. Constant angular momentum is extremely useful when dealing with the orbits of planets and satellites, and also when analyzing the Bohr model of the atom.
In modern (late 20th century) theoretical physics, angular momentum is described using an different formalism. Under this formalism, angular momentum is the 2-form Noether charge associated with rotational invariance (As a result, angular momentum isn't defined for general curved spacetimes, unless it happens to be asymptotically rotationally invariant). For a system of point particles without any intrinsic angular momentum, it turns out to be