14.10 : Principle of Angular Impulse and Momentum

The angular impulse and momentum principle provides insights into how forces applied at a distance from an object's rotational axis influence its angular velocity. It builds upon the crucial relationship between the moment of force and angular momentum. By integrating this equation, substituting the limits for the initial and final times, a comprehensive expression representing the angular impulse and momentum principle is derived.

This principle encapsulates the definition of initial and final angular momenta as moments of the particle's linear momentum at specific instants. The calculation of angular impulse involves integrating the moments of all forces acting on the particle over time. The versatility of this equation extends to systems of particles, with each term defined for every individual particle. In situations where particle motion is confined to the x-y plane, three scalar equations can succinctly express the dynamics.

A noteworthy application arises in the conservation of angular momentum, observed when the cumulative angular impulses acting on a particle sum up to zero. A practical illustration is found in a spinning flywheel, which adeptly maintains its momentum by strategically altering its rotational speed. This nuanced understanding of the angular impulse and momentum principle unveils the intricate interplay of forces, moments, and angular velocities, enriching our comprehension of rotational dynamics in diverse physical systems.