Angular Momentum of a Rotating Particle
Applying a torque to a particle about a given axis imparts an angular momentum that is not necessarily along the same axis. This is illustrated in this Demonstration for a particle of unit mass. You can vary the initial particle position and the angular velocity vector . The position vector (indicated by the black sphere), the velocity , and the angular momentum all rotate as a function of time about the axis .
The rotation of the particle is performed using the Mathematica built-in function RotationMatrix.
For more information, see Chapter 10 in  and Chapter 11 in .
 J. R. Taylor, Classical Mechanics, Sausalito, CA: University Science Books, 2005.
 S. T. Thornton and J. B. Marion, Classical Dynamics of Particles and Systems, Belmont, CA: Brooks/Cole, 2004.