Introduction

The centroid is a term that is relevant for symmetrical figures/objects and lies at the center of the said object. The determination of the centroid of a figure differs for different objects. For instance, the centroid of a triangle is the point where all three of its medians intersect.

On the other hand, a center of gravity exists for every object regardless of its symmetry and it can even lie outside the object. Determination of center of gravity involves weight-distance analysis. Interestingly, for symmetrical objects, the centroid and the center of gravity are the same.

Irregularly placed stones.

Centroid of trapezium

Understanding and studying centroids and the center of gravity is important for knowing whether a system or object is stable or not. For example, in the image above, the center of gravity of the stones will tend to shift towards the left since there are more stones towards that side, making it unstable. This article will discuss these concepts in detail.

Center Of Gravity

In simplest terms, the center of gravity is that point of an object at which it is acted upon by the gravitational force. We can assume the entire weight of the object to be concentrated at this point and for a lot of scenarios, treat the object as a point mass situated at its center of gravity (but not always).

The figure below shows the concept of center of gravity in detail.

Center of gravity

The location of the center of gravity makes a huge difference in the stability of objects. Systems that have a COG close to the ground tend to have better stability and do not topple over easily. On the other hand, systems with a high-lying COG can topple over quite easily when given a small push.

Equation For Centre Of Gravity

There is no universal formula for the determination of center of gravity but we list a simple one here. If a massless rod has two weights placed on its ends at distances x1  and x2, then the COG lies at a distance given by:

Relation Between Centre Of Gravity And Centre Of Mass

The concepts of center of mass and center of gravity are closely related and often at times, they lie at the same point. However, the center of mass is that point where the entire mass of the system can be supposed to be concentrated when it is acted upon by any force in any direction. On the other hand, the center of gravity is exclusively connected to the gravitational force.

Practice Problems

1. Find the centroid of a straight line of length 10m?

For a straight, uniform line, the centroid lies at the center. Thus,

2. Find the centroid of a circle of area A?

Regardless of the area of the circle, the centroid of a circle lies at its geometrical center.

3. Find the centroid of a rectangle of length a and breadth b?

If the length of the rectangle is taken along the X-direction and the breadth along the Y-direction, then the centroid lies at the point given by .

What is Centroid?

The centroid refers to the centers of geometrical figures regardless of the distribution of mass. It is a geometrical concept whose location does not change even if the object in question is heavier on one side and lighter on the other.

Difference Between Centre Of Gravity And Centroid 

Summary

This article discussed two interesting concepts, namely, the center of gravity and the centroid. These topics are both related to the stability and balance of a system but differ in definition and characteristics.

The center of gravity is that point where the force of gravity acts. On the other hand, the centroid is the geometrical center of an object. This article also discussed example problems to better elucidate these topics.

Frequently Asked Questions

1. How can you find the centroid of a sphere?

The sphere is a symmetrical figure whose centroid lies on its center. If it is placed with its center at the origin, the centroid is the origin itself.

2. What is the unit of the center of gravity?

The center of gravity is a location whose position can be determined with reference to an origin in meters.

3. Where should batteries be placed in electric vehicles?

Batteries are heavy and thus, must be placed as low as possible to provide better stability.