14.10:
Principle of Angular Impulse and Momentum
The angular impulse and momentum principle explains how forces applied at a distance from the rotational axis can affect an object's angular velocity.
Recall the relationship between the moment of force and angular momentum.
Integrating the equation, substituting the limits, and rearranging the terms, an equation that represents the principle of angular impulse and momentum is derived.
Here, initial and final angular momenta are defined as the moments of the particle's linear momentum at specific instances.
The angular impulse is calculated by integrating the moments of all forces acting on the particle over time.
The same equation can be extended to a system of particles, where each term is defined for every particle.
If particle motion is restricted to the x-y plane, it can be expressed using three scalar equations.
Conservation of angular momentum occurs when the sum of angular impulses acting on particles is zero.
An example is a spinning merry-go-round where, upon changing its mass, it changes its speed of rotation to maintain its angular momentum.
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.