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Newton's Law of Gravitational Attraction01:24

Newton's Law of Gravitational Attraction

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Sir Isaac Newton established the universality of the law of gravitational attraction based on empirical evidence and inductive reasoning. He published his work in Philosophiae Naturalis Principia Mathematica ("the Principia") on July 5, 1687.
Newton's law of gravitational attraction is a fundamental law of physics that governs the attraction between objects. It states that the magnitude of the gravitational force between any two objects is proportional to their masses and inversely...
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Newton's Law of Gravitation01:15

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Our everyday observation tells us that all objects close to the Earth naturally tend to fall to the ground. Early philosophers assumed that this downward force was unique to Earth. By the 16th century, Nicolaus Copernicus (1473-1543) put forward the heliocentric theory, which suggested that Earth and other planets orbited the sun, while the Moon orbited the Earth. However, it was Isaac Newton (1642-1727) who linked these two motions together in the 17th century. He reasoned that the force of...
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Frictional Force01:07

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When a body is in motion, it encounters resistance because the body interacts with its surroundings. This resistance is known as friction, a common yet complex force whose behavior is still not completely understood. Friction opposes relative motion between systems in contact, but also allows us to move. Friction arises in part due to the roughness of surfaces in contact. For one object to move along a surface, it must rise to where the peaks of the surface can skip along the bottom of the...
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The Principle of Superposition and the Gravitational Field01:17

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The principle of superposition applies to gravitational forces of objects that are sufficiently far apart. It states that the net gravitational force on a point object is the vector sum of the gravitational forces on it due to various objects. The principle helps calculate the force by listing the individual forces and then vectorially summing them up. However, it should be noted that the principle of superposition is not always apparent. In the presence of a second force, the first force could...
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Principle of Equivalence01:18

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According to Albert Einstein (1897-1955), free-falling and feeling weightless are intrinsically linked. If a person were in free-fall under gravity, for example, diving towards the Earth from an airplane, they would feel completely weightless. Similarly, a person descending in a lift may feel partially weightless. Broadly speaking, it is assumed that an object in a uniform gravitational field and an object undergoing constant acceleration in the absence of gravity are under the same...
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Dry Friction01:30

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Dry friction occurs between two solid surfaces in contact as they attempt to move relative to one another. In daily life, dry friction is encountered in various forms, such as when walking on the ground, sliding an object across a table, or rubbing hands together. Despite its ubiquity, the underlying mechanisms behind dry friction are not readily visible.
To illustrate this concept, imagine a wooden crate resting on a rough, non-uniform horizontal surface. When an external force is applied to...
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Related Experiment Video

Updated: Jul 25, 2025

Atomic Force Microscopy Cantilever-Based Nanoindentation: Mechanical Property Measurements at the Nanoscale in Air and Fluid
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Atomic Force Microscopy Cantilever-Based Nanoindentation: Mechanical Property Measurements at the Nanoscale in Air and Fluid

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Gravitational friction from d'Alembert's principle.

C Ortiz1, Raju S Khatiwada2

  • 1Unidad Académica de Física, Universidad Autónoma de Zacatecas, 98060, Zacatecas, México. ortizgca@fisica.uaz.edu.mx.

Scientific Reports
|June 26, 2023
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Summary

This study explores energy loss in particles due to gravity under non-holonomic constraints, extending physics principles beyond holonomic limitations. Findings confirm energy dissipation and align with continuum mechanics for broader applicability.

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Area of Science:

  • Theoretical Physics
  • Classical Mechanics
  • Continuum Mechanics

Background:

  • The least action principle is fundamental in modern physics but limited to holonomic constraints.
  • Investigating physics under non-holonomic constraints is crucial for broader theoretical development.

Purpose of the Study:

  • To investigate energy loss of particles interacting gravitationally in a medium with non-holonomic constraints.
  • To extend the applicability of physical principles to systems with non-holonomic constraints.
  • To analyze energy dissipation for arbitrary particles, with a specific focus on photons.

Main Methods:

  • Calculation from first principles using the principle of virtual work.
  • Application of d'Alembert principle for analyzing forces under constraints.
  • Utilizing continuum mechanics and the Euler-Cauchy stress principle for an alternative derivation.

Main Results:

  • Established the dissipative nature of energy loss under non-holonomic constraints.
  • Derived the energy lost by arbitrary particles, including a specific result for photons.
  • Confirmed consistency between the first-principles derivation and the continuum mechanics approach.

Conclusions:

  • The study successfully extends the analysis of energy loss to non-holonomic systems.
  • The findings demonstrate the dissipative effects of gravitational interaction under these constraints.
  • The agreement with continuum mechanics validates the robustness of the derived formalism.