Baryons and their quark constituents

[Atomos]

I have been given an assingment where I must show that the properties of the up, down and strange quarks follow from the properties of the baryons. I am just wondering why delta +1 (a baryon) has a spin 3/2 when it is, like a proton, composed of up, up, down. Aren't spins additive? and how do all of the 3/2 and 1/2 spin baryons follow from the combination of the up, down, and strange quarks alone? I can count only 10 combinations of those 3 types.

 

[Dick]

If you think spins are additive in the sense of 1/2+1/2+1/2=3/2 you would be wrong. And if you do think this you should be wondering why the proton has spin 1/2 rather than 3/2. A system of three spin 1/2 particles can be in a total spin state of either 1/2 or 3/2.

 

[mjsd]

spins are "additive" but they are not numbers, they are spinors. addition rules are different.. but still makes a lot sense, eg. spin +1/2 and spin -1/2 adds to spin 0 (this is just means the spins of the two constitutents are anti-align. so with 3 spins states, you can have $$\pm 1/2 \text{or} \pm 3/2$$ that means you get a spin 1/2 or 3/2 particle.