14.10 : 角冲量和动量原理

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.