Draw a cone diagram, as in Figure, showing the spin states of a particle with s = 1/2. Repeat for a particle with s = 3/2. Draw both diagrams on the same scale, and be as accurate as you can with magnitudes and directions.
Figure: A particle with well-defined and Lz has completely undefined Lx and Ly, so we can visualize its angular momentum “vector” as a cone, smeared over all possible Lx and Ly values. Shown here are the allowed states for ℓ = 1 and ℓ = 2.
Free body diagram