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Related Concept Videos

Frictional Force01:07

Frictional Force

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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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Static and Kinetic Frictional Force01:05

Static and Kinetic Frictional Force

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One of the simpler characteristics of sliding friction is that it is parallel to the contact surfaces between systems, and is always in a direction that opposes the motion or attempted motion of the systems relative to each other. If two systems are in contact and moving relative to one another, then the friction between them is called kinetic friction. For example, kinetic friction slows a hockey puck sliding on ice.
However, if two systems are in contact and are stationary relative to one...
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Stokes' Law01:20

Stokes' Law

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Viscous forces, like friction, are intermolecular forces that resist the relative motion of molecules over each other. When a solid body moves through a liquid, viscous forces drag it in the opposite direction. The force's magnitude depends on the solid's shape and size, as well as its speed and the liquid's coefficient of viscosity, density and temperature.
The expression for the force on a solid spherical object in a fluid is called Stokes' law. Stokes' law is valid only...
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Non-conservative Forces01:17

Non-conservative Forces

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Non-conservative forces are dissipative forces such as friction or air resistance. These forces take energy away from a system as it progresses. Unlike conservative forces, non-conservative forces do not have potential energy associated with them. This is because the energy is lost to the system and cannot be turned into useful work later.
Also unlike their conservative counterparts, they are path-dependent; where the object starts and stops does matter. For example, a grinding wheel applies a...
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Equation of Motion: General Plane motion - Problem Solving01:16

Equation of Motion: General Plane motion - Problem Solving

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Consider a lawn roller with a mass of 100 kg, a radius of 0.2 meters, and a radius of gyration of 0.15 meters. A force of 200 N is applied to this roller, angled at 60 degrees from the horizontal plane. What will be the angular acceleration of the lawn roller?
The friction between the roller and the ground is characterized by two coefficients. The static friction coefficient is 0.15, while the kinetic friction coefficient is 0.1. These values are crucial in understanding the interaction between...
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Static Friction01:18

Static Friction

1.5K
Static friction is a force that opposes the relative motion or tendency of motion between two surfaces in contact. It plays a crucial role in our daily lives, from walking on the ground to driving a car.
For example, consider a scenario where a truck is connected to a car by a rope, ready to tow it along a road. When no external force is applied by the truck, the car remains stationary and is said to be in static equilibrium. In this case, the forces acting on the car, such as gravity and the...
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Updated: Mar 1, 2026

Visually Based Characterization of the Incipient Particle Motion in Regular Substrates: From Laminar to Turbulent Conditions
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Single particle Brownian motion with solid friction.

Prasenjit Das1, Sanjay Puri1, Moshe Schwartz2,3

  • 1School of Physical Sciences, Jawaharlal Nehru University, 110067, New Delhi, India.

The European Physical Journal. E, Soft Matter
|June 8, 2017
PubMed
Summary
This summary is machine-generated.

This study analyzes particle motion on vibrating surfaces using friction and noise models. We derived analytical and numerical results for particle velocity and diffusion, showing good agreement in dimensions up to three.

Keywords:
Flowing Matter: Granular Matter

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Area of Science:

  • Physics
  • Statistical Mechanics
  • Nonlinear Dynamics

Background:

  • Brownian dynamics describes particle movement influenced by random forces.
  • Solid friction and Gaussian white noise are key models for surface interactions and vibrations.
  • Understanding particle behavior in such systems is crucial for various physical phenomena.

Purpose of the Study:

  • To investigate the Brownian dynamics of a solid particle on a vibrating solid surface.
  • To model particle-surface interactions using solid friction and Gaussian white noise.
  • To derive and analyze the Fokker-Planck equation for particle probability distribution.

Main Methods:

  • Phenomenological modeling of solid friction proportional to relative velocity.
  • Derivation of the Fokker-Planck equation for probability distribution.
  • Analytical calculation of steady-state velocity distribution, mean-square velocity, and diffusion coefficient in d-dimensions.
  • Development of a generic method for calculating autocorrelations in d-dimensions.
  • Numerical computation of mean-square velocity and steady-state velocity autocorrelation up to d=3.

Main Results:

  • Analytical expressions for steady-state velocity distribution, mean-square velocity, and diffusion coefficient were derived in d-dimensions.
  • An exact evaluation of the steady-state velocity autocorrelation was achieved in one dimension.
  • General expressions enabling approximate analytic evaluation of autocorrelations in higher dimensions were presented.
  • Numerical results for mean-square velocity and autocorrelation showed good agreement with analytical findings.

Conclusions:

  • The study provides a comprehensive framework for analyzing particle dynamics on vibrating surfaces.
  • Both analytical and numerical methods confirm the validity of the derived expressions.
  • The findings offer insights into particle diffusion and velocity correlations in complex systems.