Spin and Angular Momentum

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

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 ℏ 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 = ℏ x (0,1/2,1, 3/2 ...).   The electron, a Fermion,  happens to have s = 1/2 ℏ

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)