Show that the angular momentum of a particle is the product of its linear momentum and the moment arm. Also show that the angular momentum is produced only by the angular component of linear momentum.

The angular momentum of a particle is fundamentally linked to its linear momentum and the concept of the moment arm, which is the perpendicular distance from the line of action of the linear momentum to the axis of rotation. Angular momentum can be defined as the product of the particle’s linear momentum and this moment arm. This relationship points out how the rotational effect of a particle is dependent, not only on its velocity but also on its distance from the axis about which it rotates.

In addition, it is worthwhile to note that angular momentum results purely from the angular component of linear momentum. The linear momentum of a particle can be divided into two components. One component is along the radius, known as the radial component, and the other is perpendicular to the radius, known as the tangential component. Since the radial component acts along the radius, it does not contribute to angular momentum because it does not produce any rotational effect. The tangential component of the linear momentum would be the one that impacts the angular momentum as it creates rotation around the axis.

Angular momentum is thus the product of the linear momentum and the moment arm, and only the tangential component of linear momentum produces the motion in an angular direction.

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