14.9:
Relation Between Moment of a Force and Angular Momentum
In a spinning top, applying a force at a distance from the center creates torque, which changes the angular momentum of the top, causing it to spin.
The moment of a force is the rotational equivalent of linear force. It measures how a force on an object induces rotation.
Angular momentum is the rotational analog of linear momentum and signifies the tendency of an object to continue rotating.
The time derivative of angular momentum gives an expression, in which the first term equals zero. The second term can be expressed in terms of the net force acting on the particle.
Comparing the expression with the moment of force equation establishes a relation between the angular momentum and the moment of force.
This relationship mirrors Newton's second law but for rotational motion.
This equation applies equally to the systems of particles or rigid bodies.
In a system of particles, each particle contributes to the overall angular momentum of the system.
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.