# Q & A: Spin and angular momentum

Q:
What does spin 1/2 physically signify..? Is it something related to Angular Momentum of the fermion..????
- Mrinmoy (age 18)
assam, India
A:

There are two kinds of angular momentum, both classically and quantum mechanically.  The earth-sun system is a good classical example.   The earth orbits the sun once per year and has orbital angular momentum proportional to the earth-sun distance times the relative velocity of the earth perpendicular to the earth-sun distance.  It is a vector quantity.   In addition the earth can have spin angular momentum proportional to the inverse of the length of a day times a quantity called the moment of inertia.    Likewise in quantum mechanics you can have these two kinds of angular momenta, orbital and spin .

The major difference is that classically these quantities can be any value, whereas in quantum mechanics the orbital kind must be an integer times which is Plank's constant divided by 2π. See:   Curiously, the values of spin angular momentum, s,  can have half-integer values, e.g. s = x (0,1/2,1, 3/2 ...).   The electron, a Fermion,  happens to have s = 1/2

So when someone says that "electrons have spin 1/2"  they imply the value in units of h-bar.

LeeH

So the classical distinction between the two types of angular momentum is a bit arbitrary, depending on how you choose to break up your description of objects into spinning wholes vs. orbiting parts. As Lee points out, quantum mechanically there's a real qualitative difference between the orbital and spin components. /mw

(published on 08/27/2013)