Explain how angular momentum can be expressed as the vector product of two vectors. How is its direction determined? Discuss the cases of minimum and maximum angular momentum.
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The answer is in a new conserved quantity, since all of these scenarios are in closed systems. This new quantity, angular momentum, is analogous to linear momentum. In this chapter, we first define and then explore angular momentum from a variety of viewpoints. First, however, we investigate the angular momentum of a single particle. This allows us to develop angular momentum for a system of particles and for a rigid body that is cylindrically symmetric.
with respect to the origin. Even if the particle is not rotating about the origin, we can still define an angular momentum in terms of the position vector and the linear momentum.
Angular Momentum of a Particle
The angular momentum of a particle is defined as the cross-product of
and is perpendicular to the plane containing
An x y z coordinate system is shown in which x points out of the page, y points to the right and z points up. The vector r points from the origin to a point in the x y plane, in the first quadrant. The vector points from the tip of the r vector, at an angle of theta counterclockwise from the r vector direction, as viewed from above. Both r and p vectors are in the x y plane. The vector l points up, and is perpendicular to the x y plane, consistent with the right hand rule. When the right hand has its fingers curling counterclockwise as viewed from above, the thumb points up, in the direction of l. We are also shown the components of the vector r parallel and perpendicular to the p vector. The vector r sub perpendicular is the projection of the r vector perpendicular to the p vector direction.