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Mechanical Equilibrium

Published: 2015/08/22

Channel: PhysicsandAstronomy UKY

Thermodynamics Equilibrium- Chemical, Mechanical and Thermal Equilibrium-

Published: 2015/12/19

Channel: Ujjwal Kumar Sen

CHAPTER # 2 MECHANICAL EQUILIBRIUM HEWITT

Published: 2015/06/11

Channel: Jan Rothschild

Mechanical Equilibrium Screencast

Published: 2015/08/07

Channel: ScienceMrLash

Mechanical Equilibrium

Published: 2012/08/28

Channel: Nancy Foote

Hewitt-Drew-it! PHYSICS 1. Equilibrium Rule Hewitt-Drew-it!

Published: 2012/07/11

Channel: mellenstei

Example of Mechanical equilibrium with torque

Published: 2010/10/29

Channel: Mr Bdubs Math and Physics

Introduction to Equilibrium

Published: 2015/06/19

Channel: Flipping Physics

Lecture 01 Mechanical Equilibrium: Dynamic and Static Equilibrium

Published: 2013/10/06

Channel: TDarcyPhysics

Mechanical Equilibrium

Published: 2014/02/18

Channel: jkruz1675

What is MECHANICAL EQUILIBRIUM? What does MECHANICAL EQUILIBRIUM mean?

Published: 2016/10/12

Channel: The Audiopedia

Thermodynamics 34 Mechanical Equilibrium and Ideal Gas Law

Published: 2015/09/18

Channel: Des Chimistes

Static Equilibrium, or What to do when nothing at all is happening | Doc Physics

Published: 2012/09/25

Channel: Doc Schuster

AS Physics Solving Equilibrium Problems

Published: 2014/01/25

Channel: Kate Wainwright

Balancing Torques (mechanical equilibrium)

Published: 2011/11/03

Channel: Gregory Mack

Lecture 01 Mechanical Equilibrium Problem Solving

Published: 2013/10/05

Channel: TDarcyPhysics

Mechanical Engineering: Particle Equilibrium (1 of 19) Addition of Forces - Graphically

Published: 2015/06/18

Channel: Michel van Biezen

mechanical equilibrium examples

Published: 2015/10/11

Channel: Andrew Berryman

Mechanical Engineering: Particle Equilibrium (7 of 19) Tension of Cables Attached to Hanging Object

Published: 2015/06/20

Channel: Michel van Biezen

Exam 1 Problem 1 (Boiling at Elevated Pressures and Mechanical Equilibrium)

Published: 2016/03/15

Channel: UF Teaching Center

MCAT Force Equilibrium and Free Body Diagrams

Published: 2015/02/18

Channel: Leah4sciMCAT

Thermodynamic Equilibrium

Published: 2013/02/17

Channel: chunkan yu

Mechanical Engineering: Particle Equilibrium (2 of 19) Addition of Forces - Component

Published: 2015/06/18

Channel: Michel van Biezen

Mechanical Engineering: Particle Equilibrium (13 of 19) Pulleys and Mechanical Advantage

Published: 2015/06/23

Channel: Michel van Biezen

Mechanical Engineering: Particle Equilibrium (11 of 19) Why are Pulleys a Mechanical Advantage?

Published: 2015/06/23

Channel: Michel van Biezen

Mechanical Engineering: Equilibrium of Rigid Bodies (6 of 30) Find F=? M=? Ex.1, 2-Dimensions

Published: 2015/08/23

Channel: Michel van Biezen

Mechanical Engineering: Particle Equilibrium (12 of 19) Pulleys and Mechanical Advantage

Published: 2015/06/23

Channel: Michel van Biezen

Example of Mechanical equilibrium with torque #2

Published: 2010/10/29

Channel: Mr Bdubs Math and Physics

Netural Stable Unstable Equilibrium Mechanical Engineering Lectures Notes

Published: 2015/10/08

Channel: iProf India

Mechanical Engineering: Particle Equilibrium (9 of 19) Forces on a Bracket

Published: 2015/06/20

Channel: Michel van Biezen

力學平衡mechanical equilibrium

Published: 2013/12/15

Channel: ineedlucky

Unit 4 Lesson 3: Mechanical Equilibrium

Published: 2016/11/28

Channel: Ian McNair

Mechanical Engineering: Equilibrium of Rigid Bodies (1 of 30) Introduction

Published: 2015/08/18

Channel: Michel van Biezen

Mechanical Engineering: Equilibrium of Rigid Bodies (9 of 32) Find F=? M=? Ex.4, 2-Dimensions

Published: 2015/08/26

Channel: Michel van Biezen

Static Equilibrium Problems (part II)

Published: 2009/10/17

Channel: lasseviren1

Chapter 2 and 3 Particle Equilibrium Dot product, 3-D Particle Equilibrium

Published: 2015/04/30

Channel: STATICS THE EASY WAY

Mechanical Engineering: Particle Equilibrium (17 of 19) Determining Angles in 3-Dimension

Published: 2015/06/25

Channel: Michel van Biezen

Ladder Example for Static Equilibrium

Published: 2013/09/30

Channel: cstephenmurray

Rotational Equilibrium Problems

Published: 2015/02/19

Channel: Daniel M

Mechanical Engineering: Particle Equilibrium (5 of 19) Beam and Cable Under Tension

Published: 2015/06/19

Channel: Michel van Biezen

Static and Dynamic Equilibrium

Published: 2012/12/22

Channel: AK LECTURES

Mechanical Engineering: Equilibrium of Rigid Bodies (2 of 30) Forces & Moments at Connections 1

Published: 2015/08/19

Channel: Michel van Biezen

Mechanical Engineering: Equilibrium of Rigid Bodies (5 of 30) Finding Contact Forces

Published: 2015/08/22

Channel: Michel van Biezen

Engineering Mechanics (MSBTE) - Equilibrium

Published: 2015/12/16

Channel: No - KT

Translational Equilibrium

Published: 2012/09/07

Channel: Vector Shock

Mechanical Engineering: Equilibrium of Rigid Bodies (3 of 30) Forces & Moments at Connections 2

Published: 2015/08/20

Channel: Michel van Biezen

A Level Physics: Mechanics: Forces in Equilibrium

Published: 2016/02/23

Channel: Burrows Physics

Physics, Static Equilibrium, Hanging Sign No. 5

Published: 2014/12/07

Channel: Step-by-Step Science

Mechanical Engineering: Particle Equilibrium (14 of 19) Vectors in 3-Dimensions Explained

Published: 2015/06/24

Channel: Michel van Biezen

Mechanical Engineering: Equilibrium of Rigid Bodies (4 of 30) Forces & Moments at Connections 3

Published: 2015/08/21

Channel: Michel van Biezen

From Wikipedia, the free encyclopedia

In classical mechanics, a particle is in **mechanical equilibrium** if the net force on that particle is zero.^{[1]}^{:39} By extension, a physical system made up of many parts is in mechanical equilibrium if the net force on each of its individual parts is zero.^{[1]}^{:45–46}^{[2]}

In addition to defining mechanical equilibrium in terms of force, there are many alternative definitions for mechanical equilibrium which are all mathematically equivalent. In terms of momentum, a system is in equilibrium if the momentum of its parts is all constant. In terms of velocity, the system is in equilibrium if velocity is constant. In a rotational mechanical equilibrium the angular momentum of the object is conserved and the net torque is zero.^{[2]} More generally in conservative systems, equilibrium is established at a point in configuration space where the gradient of the potential energy with respect to the generalized coordinates is zero.

If a particle in equilibrium has zero velocity, that particle is in static equilibrium.^{[3]}^{[4]} Since all particles in equilibrium have constant velocity, it is always possible to find an inertial reference frame in which the particle is stationary with respect to the frame.

An important property of systems at mechanical equilibrium is their stability.

If we have a function which describes the system's potential energy, we can determine the system's equilibria using calculus. A system is in mechanical equilibrium at the critical points of the function describing the system's potential energy. We can locate these points using the fact that the derivative of the function is zero at these points. To determine whether or not the system is stable or unstable, we apply the second derivative test:

- Second derivative < 0
- The potential energy is at a local maximum, which means that the system is in an unstable equilibrium state. If the system is displaced an arbitrarily small distance from the equilibrium state, the forces of the system cause it to move even farther away.

- Second derivative > 0
- The potential energy is at a local minimum. This is a stable equilibrium. The response to a small perturbation is forces that tend to restore the equilibrium. If more than one stable equilibrium state is possible for a system, any equilibria whose potential energy is higher than the absolute minimum represent metastable states.

- Second derivative = 0 or does not exist
- The state is neutral to the lowest order and nearly remains in equilibrium if displaced a small amount. To investigate the precise stability of the system, higher order derivatives must be examined. The state is unstable if the lowest nonzero derivative is of odd order or has a negative value, stable if the lowest nonzero derivative is both of even order and has a positive value, and neutral if all higher order derivatives are zero. In a truly neutral state the energy does not vary and the state of equilibrium has a finite width. This is sometimes referred to as state that is marginally stable or in a state of indifference.

When considering more than one dimension, it is possible to get different results in different directions, for example stability with respect to displacements in the *x*-direction but instability in the *y*-direction, a case known as a saddle point. Generally an equilibrium is only referred to as stable if it is stable in all directions.

Sometimes there is not enough information about the forces acting on a body to determine if it is in equilibrium or not. This makes it a statically indeterminate system.

A stationary object (or set of objects) is in "static equilibrium," which is a special case of mechanical equilibrium. A paperweight on a desk is an example of static equilibrium. Other examples include a rock balance sculpture, or a stack of blocks in the game of Jenga, so long as the sculpture or stack of blocks is not in the state of collapsing.

Objects in motion can also be in equilibrium. A child sliding down a slide at constant speed would be in mechanical equilibrium, but not in static equilibrium (in the reference frame of the earth or slide).

Another example of mechanical equilibrium is a person pressing a spring to a defined point. He or she can push it to an arbitrary point and hold it there, at which point the compressive load and the spring reaction are equal. In this state the system is in mechanical equilibrium. When the compressive force is removed the spring returns to its original state.

The minimal number of static equilibria of homogeneous, convex bodies (when resting under gravity on a horizontal surface) is of special interest. In the planar case, the minimal number is 4, while in three dimensions one can build an object with just one stable and one unstable balance point.^{[citation needed]} Such an object is called a gomboc.

- ^
^{a}^{b}John L Synge & Byron A Griffith (1949).*Principles of Mechanics*(2nd ed.). McGraw-Hill. - ^
^{a}^{b}Beer FP, Johnston ER, Mazurek DF, Cornell PJ, and Eisenberg, ER (2009).*Vector Mechanics for Engineers: Statics and Dynamics*(9th ed.). McGraw-Hill. p. 158. **^**Herbert Charles Corben & Philip Stehle (1994).*Classical Mechanics*(Reprint of 1960 second ed.). Courier Dover Publications. p. 113. ISBN 0-486-68063-0.**^**Lakshmana C. Rao; J. Lakshminarasimhan; Raju Sethuraman; Srinivasan M. Sivakumar (2004).*Engineering Mechanics*. PHI Learning Pvt. Ltd. p. 6. ISBN 81-203-2189-8.

- Marion JB and Thornton ST. (1995)
*Classical Dynamics of Particles and Systems.*Fourth Edition, Harcourt Brace & Company.

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