Physics Lesson 6.1.3 - Types of Equilibrium

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Welcome to our Physics lesson on Types of Equilibrium, this is the third lesson of our suite of physics lessons covering the topic of Centre of Mass. Types of Equilibrium, you can find links to the other lessons within this tutorial and access additional physics learning resources below this lesson.

Types of Equilibrium

Not all objects are equally stable when they are at rest. Some objects are more stable and they hardly move from their position when a force acts on them. On the other hand, for some other objects it a very small force is enough to make it fall sideways. In this paragraph, all possible types of equilibrium and their features are given.

1. Stable equilibrium

In this kind of equilibrium, objects are very stable. If a small force acts on them, they shake around but finally they regain the initial position. Below, two examples of stable equilibrium are shown.

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The cone will shake around for a while when a small force F acts laterally on it, but eventually it will stop at the original position. If we want to make it fall sideways, we must apply a large force.

Another example of stable equilibrium is a ball moving inside a half-spherical hollow as shown below.

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The common feature of these two examples is that they both have the centre of gravity in the lower half of the system. Indeed, the cone has the centre of gravity at 1/3 of its height as stated earlier. Also, it is obvious that the centre of gravity of the small sphere is much below than half the radius of the half-sphere. Look at the figure:

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Hence, if we take the vertical axis (the y-axis) that starts from zero at ground level and goes upwards as reference, the condition to have stable equilibrium is

yC < 1/2 h

2. Unstable equilibrium

Unstable equilibrium is the opposite of stable equilibrium, i.e. a very small force is enough to make an object topple sideways. In other words, a much greater effort is needed to re-establish the equilibrium than to distort it. Look at the figure:

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From the figure, it is clear that centre of mass is above half of the object's height. Therefore, the condition to have unstable equilibrium is

yC > 1/2 h

3. Neutral equilibrium

In this kind of equilibrium when using a force to distort the equilibrium of an object, it turns again at the original position when applying the same force but in opposite direction as before. Geometrically, centre of mass is at the same level as half the height of the object, i.e. centre of mass is at middle of the object. Look at the figure:

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Sphere and cube are the two most outstanding examples of neutral equilibrium. In both of them,

yC = 1/2 h

Example 1

Find the type of equilibrium for the objects shown below.

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Solution 1

a.The ball is in unstable equilibrium as its centre of gravity is above the half-sphere, i.e. much higher than half radius as shown below.

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b.The object shown in the figure is in stable equilibrium as since it is wider in the lower part, its centre of mass is below half of height.

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c.This object is in unstable equilibrium since it is wider in the upper part, so its centre of mass is above half of height.

Physics Tutorials: This image provides visual information for the physics tutorial Centre of Mass. Types of Equilibrium

d.This object is in neutral equilibrium as its centre of mass is at the level of half-height.

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You have reached the end of Physics lesson 6.1.3 Types of Equilibrium. There are 6 lessons in this physics tutorial covering Centre of Mass. Types of Equilibrium, you can access all the lessons from this tutorial below.

More Centre of Mass. Types of Equilibrium Lessons and Learning Resources

Centre of Mass and Linear Momentum Learning Material
Tutorial IDPhysics Tutorial TitleTutorialVideo
Tutorial
Revision
Notes
Revision
Questions
6.1Centre of Mass. Types of Equilibrium
Lesson IDPhysics Lesson TitleLessonVideo
Lesson
6.1.1What is Centre of Mass?
6.1.2How to Determine the Centre of Mass in Objects?
6.1.3Types of Equilibrium
6.1.4When Does an Object Start Falling Sideways?
6.1.5More Stable and Less Stable within Neutral
6.1.6The Importance of Centre of Mass in Physics

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