14.9 : Relation Between Moment of a Force and Angular Momentum

In the realm of spinning tops, the application of force at a distance from the center produces torque, a pivotal factor that alters the angular momentum of the top, thereby inducing its rotation. The concept of moment, akin to linear force in rotation, quantifies how a force acting upon an object initiates rotational motion. Angular momentum serves as the rotational counterpart to linear momentum, representing an object's inherent tendency to persist in its rotational state.

The temporal change in angular momentum, when expressed as a derivative, yields an equation where the initial term is null, and the subsequent term correlates with the net force acting on the particle. A comparison of this expression with the moment of force equation establishes a crucial link between angular momentum and the moment of force, reflecting a rotational analog of Newton's second law.

This fundamental equation is universally applicable to both systems of particles and rigid bodies. Within a system of particles, the cumulative angular momentum arises from the individual contributions of each particle. In essence, this conceptual framework extends the principles of Newtonian dynamics to rotational motion, encapsulating the interplay between force, torque, and angular momentum in the dynamic world of rotating objects.