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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 .

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DETAILS

The rotation of the particle is performed using the Mathematica built-in function RotationMatrix.
For more information, see Chapter 10 in [1] and Chapter 11 in [2].
References
[1] J. R. Taylor, Classical Mechanics, Sausalito, CA: University Science Books, 2005.
[2] S. T. Thornton and J. B. Marion, Classical Dynamics of Particles and Systems, Belmont, CA: Brooks/Cole, 2004.
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