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Related Concept Videos

Equilibrium Conditions for a Particle01:23

Equilibrium Conditions for a Particle

When an object is in equilibrium, it is either at rest or moving with a constant velocity. There are two types of equilibrium: static and dynamic. Static equilibrium occurs when an object is at rest, while dynamic equilibrium occurs when an object is moving with a constant velocity. In both cases, there must be a balance of forces acting on the object.
To understand the concept of equilibrium, let us first consider the forces acting on an object. When different forces act on an object, they can...
First Law: Particles in One-dimensional Equilibrium01:10

First Law: Particles in One-dimensional Equilibrium

Newton's first law of motion states that a body at rest remains at rest, or if in motion, remains in motion at constant velocity, unless acted on by a net external force. It also states that there must be a cause for any change in velocity (a change in either magnitude or direction) to occur. This cause is a net external force. For example, consider what happens to an object sliding along a rough horizontal surface. The object quickly grinds to a halt, due to the net force of friction. If we...
First Law: Particles in Two-dimensional Equilibrium01:18

First Law: Particles in Two-dimensional Equilibrium

Recall that a particle in equilibrium is one for which the external forces are balanced. Static equilibrium involves objects at rest, and dynamic equilibrium involves objects in motion without acceleration; but it is important to remember that these conditions are relative. For instance, an object may be at rest when viewed from one frame of reference, but that same object would appear to be in motion when viewed by someone moving at a constant velocity.
Newton's first law tells us about the...
Oscillations about an Equilibrium Position01:04

Oscillations about an Equilibrium Position

Stability is an important concept in oscillation. If an equilibrium point is stable, a slight disturbance of an object that is initially at the stable equilibrium point will cause the object to oscillate around that point. For an unstable equilibrium point, if the object is disturbed slightly, it will not return to the equilibrium point. There are three conditions for equilibrium points—stable, unstable, and half-stable. A half-stable equilibrium point is also unstable, but is named so because...
Stability of Equilibrium Configuration: Problem Solving01:13

Stability of Equilibrium Configuration: Problem Solving

The stability of equilibrium configurations is an important concept in physics, engineering, and other related fields. In simple terms, it refers to the tendency of an object or system to return to its equilibrium position after being disturbed. The stability of an equilibrium configuration can be analyzed by considering the potential energy function of the system and examining its behavior near the equilibrium point.
Problem-solving in the context of the stability of equilibrium configuration...
Static Equilibrium - I01:05

Static Equilibrium - I

A rigid body is said to be in dynamic equilibrium when both its linear and angular acceleration are zero, relative to an inertial frame of reference. This means that a body in equilibrium can be moving, but only when its linear and angular velocities are constant. A rigid body is said to be in static equilibrium when it is at rest in the selected frame of reference. The distinction between static equilibrium (e.g., a state of rest) and dynamic equilibrium (e.g, a state of uniform motion) is...

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Related Experiment Video

Updated: Jul 16, 2026

Optical Trap Loading of Dielectric Microparticles In Air
08:57

Optical Trap Loading of Dielectric Microparticles In Air

Published on: February 5, 2017

Equilibrium theory for a particle pulled by a moving optical trap.

R Dean Astumian1

  • 1University of Maine, Orono, Maine 04469-5709, USA. astumian@maine.edu

The Journal of Chemical Physics
|March 27, 2007
PubMed
Summary

Optical traps use mechanical force to pull colloidal particles through solutions. Rapid equilibration allows modeling via equilibrium theory, simplifying analysis of nanoscale machines like molecular motors.

Area of Science:

  • Physics, Soft Matter
  • Statistical Mechanics
  • Nanotechnology

Background:

  • Colloidal particles in optical traps experience significant viscous drag.
  • Rapid mechanical equilibration is observed on experimentally relevant timescales.
  • This system can be modeled using equilibrium theory despite energy dissipation.

Purpose of the Study:

  • To model the dynamics of a colloidal particle in an optical trap.
  • To analyze the effects of energy dissipation in a non-equilibrium system.
  • To generalize equilibrium concepts to nanoscale machines.

Main Methods:

  • Applying equilibrium theory to a system with viscous drag.
  • Utilizing coordinate transformations to a stationary frame of reference.

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Fabrication and Operation of a Nano-Optical Conveyor Belt

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Optical Trapping of Nanoparticles
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Optical Trapping of Nanoparticles

Published on: January 15, 2013

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Last Updated: Jul 16, 2026

Optical Trap Loading of Dielectric Microparticles In Air
08:57

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Published on: February 5, 2017

Fabrication and Operation of a Nano-Optical Conveyor Belt
11:10

Fabrication and Operation of a Nano-Optical Conveyor Belt

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Optical Trapping of Nanoparticles
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Optical Trapping of Nanoparticles

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  • Analyzing stochastic dynamics using Onsager-Machlup theory.

    • Main Results:

    • Mechanical force equals viscous drag force on relevant timescales.
    • Energy dissipation effects are incorporated via coordinate transformations.
    • Stochastic dynamics in the stationary frame follow a canonical equilibrium distribution.

    Conclusions:

    • The study provides a framework for analyzing nanoscale machines.
    • Generalizations of detailed balance and fluctuation-dissipation relations are presented.
    • The model is applicable to molecular motors, pumps, and other nanoscale devices.