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Related Concept Videos

Conservation of Angular Momentum01:09

Conservation of Angular Momentum

A system's total angular momentum remains constant if the net external torque acting on the system is zero. Considering a system that consists of n tiny particles, the angular momentum of any tiny particle may change, but the system's total angular momentum would remain constant. The principle of conservation of angular momentum only considers the net external torque acting on the system. While there are internal forces exerted by different particles within the system that also produce internal...
Angular Momentum01:21

Angular Momentum

Angular momentum characterizes an object's rotational motion and is defined as the moment of its linear momentum about a specified point O. When a particle moves along a curved path in the x-y plane, the scalar formulation calculates the magnitude of its angular momentum, utilizing the moment arm (d), representing the perpendicular distance from point O to the line of action of the linear momentum. Despite being scalar in formulation, angular momentum is inherently a vector quantity. Its...
Angular Momentum about an Arbitrary Axis01:11

Angular Momentum about an Arbitrary Axis

Imagine a rigid body with a mass denoted as 'm', which has its center of mass at point G and is rotating around an inertial reference frame. The angular momentum at an arbitrary point P can be calculated by taking the cross product of the position vector and linear momentum vector for each individual mass element.
The velocity of a mass element comprises its translational velocity and the relative velocity instigated by the body's rotation. Substituting the velocity equation into the angular...
Principle of Angular Impulse and Momentum: Problem Solving01:19

Principle of Angular Impulse and Momentum: Problem Solving

Consider a ball of mass m, attached to a massless rod of known length, subjected to a time-dependent torque. If the initial velocity of the mass is known, then the final velocity of the mass for time t can be determined using the principle of angular impulse and momentum.
Initially, a free-body diagram of the system is drawn to illustrate all the forces acting upon the system, providing a crucial understanding of the dynamics at play. Then, the principle of angular impulse and momentum is...
Principle of Angular Impulse and Momentum01:23

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.
Euler Equations of Motion01:19

Euler Equations of Motion

Imagine a rigid body that is rotating at an angular velocity of ω within an inertial frame of reference. Along with this, picture a second rotating frame that is attached to the body itself. This frame moves along with the body and possesses an angular velocity of Ω. The total moment about the center of mass is calculated by adding the rate of change of angular momentum about the center of mass in relation to the rotating frame and the cross-product of the body's angular velocity and its...

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Related Experiment Video

Updated: Jul 3, 2026

Experimental Methods to Study Human Postural Control
08:12

Experimental Methods to Study Human Postural Control

Published on: September 11, 2019

Exact solution to ideal chain with fixed angular momentum.

J M Deutsch1

  • 1Department of Physics, University of California, Santa Cruz, California 95064, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|July 23, 2008
PubMed
Summary
This summary is machine-generated.

We studied polymer chains with fixed angular momentum (L). The radius of gyration for ring polymers was exactly derived, showing it differs from random walks even at L=0.

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Area of Science:

  • Statistical mechanics
  • Polymer physics
  • Theoretical chemistry

Background:

  • Understanding polymer behavior is crucial in various scientific fields.
  • The influence of angular momentum on polymer conformation is not well-understood.

Purpose of the Study:

  • To investigate the statistical mechanics of a noninteracting polymer chain with fixed total angular momentum (L).
  • To derive the radius of gyration for a ring polymer under these conditions.

Main Methods:

  • Utilized functional integration techniques.
  • Analyzed a noninteracting polymer chain in the limit of a large number of monomers.
  • Considered the case of fixed total angular momentum (L).

Main Results:

  • Derived the radius of gyration for a ring polymer in closed form.
  • Found that the radius of gyration differs from a random walk by a prefactor of order unity, even when L=0.
  • Qualitatively discussed the dependence of the radius of gyration on L.

Conclusions:

  • The derived formula provides an exact solution for the radius of gyration of a ring polymer with fixed angular momentum.
  • The results offer insights into polymer behavior under constrained conditions.
  • The findings can be extended to understand self-avoiding polymer chains.