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Conservation of Angular Momentum: Application01:18

Conservation of Angular Momentum: Application

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A system's total angular momentum remains constant if the net external torque acting on the system is zero. Examples of such systems include a freely spinning bicycle tire that slows over time due to torque arising from friction, or the slowing of Earth's rotation over millions of years due to frictional forces exerted on tidal deformations. However in the absence of a net external torque, the angular momentum remains conserved. The conservation of angular momentum principle requires a...
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Conservation of Linear Momentum for a System of Particles01:28

Conservation of Linear Momentum for a System of Particles

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In the dynamic realm of billiards, a fascinating interplay of forces governs the motion of cue balls and stationary balls. When the cue ball collides with a stationary ball, linear momentum is exchanged. The cue ball imparts a fraction of its linear momentum to the stationary ball, causing the cue ball to decelerate while initiating the motion of the stationary ball.
The impulsive force at play during this interaction is of extremely short duration, rendering its impulse negligible. When...
535
Conservation of Angular Momentum01:09

Conservation of Angular Momentum

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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...
15.9K
Linear Momentum in Control Volume01:13

Linear Momentum in Control Volume

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Newton's second law is applied to obtain the linear momentum in a control volume in a fluid system. According to this law, the rate of change of linear momentum is equal to the sum of external forces acting on the system. When a control volume matches the fluid system at a specific moment, the forces acting on both are identical. Reynolds transport theorem helps explain this by breaking down the system's linear momentum into two components: the rate of change of linear momentum within...
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Angular Momentum01:21

Angular Momentum

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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...
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Principle of Linear Impulse and Momentum for a System of Particles01:21

Principle of Linear Impulse and Momentum for a System of Particles

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In the context of a system of particles moving relative to an inertial frame of reference, the equation of motion is a crucial tool for understanding the dynamics of the system. This equation, which accounts for external forces acting on each particle, plays a fundamental role in describing the system's behavior.
Notably, internal forces between particles, occurring in equal and opposite collinear pairs, cancel out and are not part of the equation of motion. This exclusion simplifies the...
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Related Experiment Video

Updated: Jan 18, 2026

Robotic Mirror Therapy System for Functional Recovery of Hemiplegic Arms
10:32

Robotic Mirror Therapy System for Functional Recovery of Hemiplegic Arms

Published on: August 15, 2016

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A physics-informed graph neural network conserving linear and angular momentum for dynamical systems.

Vinay Sharma1, Olga Fink2

  • 1Intelligent Maintenance and Operations Systems, EPFL, Lausanne, Switzerland.

Nature Communications
|January 15, 2026
PubMed
Summary
This summary is machine-generated.

We introduce DYNAMI-CAL GRAPHNET, a novel Physics-Informed Graph Neural Network. This model accurately predicts complex multi-body dynamics, ensuring physical consistency and interpretability for real-time applications.

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Area of Science:

  • Physics
  • Computer Science
  • Engineering

Background:

  • Accurate modeling of multi-body dynamical systems is crucial for prediction and inference.
  • Traditional physics-based models struggle with scalability and computational cost.
  • Data-driven Graph Neural Networks (GNNs) often lack physical consistency and interpretability.

Purpose of the Study:

  • To propose DYNAMI-CAL GRAPHNET, a Physics-Informed Graph Neural Network.
  • To integrate GNN learning with physics-based inductive biases for improved modeling.
  • To address limitations of traditional and purely data-driven approaches in dynamical systems.

Main Methods:

  • Developed DYNAMI-CAL GRAPHNET, a novel Physics-Informed Graph Neural Network.
  • Enforced pairwise conservation of linear and angular momentum using equivariant edge-local reference frames.
  • Designed for rotational equivariance, translational invariance, and permutation equivariance.

Main Results:

  • Achieved physically consistent predictions of node dynamics.
  • Provided interpretable, edge-wise linear and angular impulses.
  • Demonstrated stable error accumulation, effective extrapolation, and robust handling of heterogeneous interactions and external forces on a 3D granular system.

Conclusions:

  • DYNAMI-CAL GRAPHNET offers accurate, interpretable, and real-time modeling of complex multi-body dynamical systems.
  • Enables inference of forces and moments while efficiently handling complex interactions.
  • Valuable for robotics, aerospace engineering, materials science, control systems, and mechanical process optimization.