The center of mass of a system of particles is a specific point at which, for many purposes, the system’s mass behaves as if it were concentrated. In another word, center of mass is the point at which the distribution of mass is equal in all directions, and does not depend on gravitational field.

The center of mass is a function only of the positions and masses of the particles that comprise the system. However, the center of gravity is the point through which the force of gravity acts on an object.

Both center of mass and center of gravity have crucial applications in mechanics of materials; simplify solution of problems of engineering mechanics.

What is the center of mass?

The center of mass is a position defined relative to system of objects. It is the average position of all the parts of the system, weighted according to their masses. In the case of a rigid body, the position of its center of mass is fixed in relation to the object.

For instance, the center of mass of a uniform disc shape would be at its center. Sometimes the center of mass does not fall anywhere on the object such as in the case of a ring in which the center of mass is located at its center, where there is not any material.

There are a couple of useful experimental tests that can be done to determine the center of mass of rigid physical objects such as table edge method which can be used to find the center of mass of small rigid objects with at least one flat side. The plumb line method is also useful for objects which can be suspended freely about a point of rotation.

The center of mass can be computed as sum of mass of part of an object times position of part of an object divided by sum of mass of an object.

Center of Mass
Fig. 1: Center of Mass
Plumb line method being used to find the center of mass of an irregular object
Fig. 2: Plumb line method being used to find the center of mass of an irregular object

Benefits of Center of Mass

One useful application of the center of mass is determining the maximum angle that an object can be tilted before it topples over.

The center of mass of an object is the point where any uniform force on the object acts. This is beneficial since it greatly simplifies problems of mechanics in which the motion of oddly-shaped objected and complicated systems need to be described.

For the purposes of calculation, an oddly-shaped object can be treated as if all its mass is concentrated in a tiny object located at the center of mass. This imaginary object is sometimes termed as point mass.

If a rigid object is pushed at its center of mass, then the object would move as if it is a point mass. The object would not rotate about any axis disregard of its actual shape. However, if unbalanced force is exerted at a point other than center of mass, then the object rotate about its center of mass.

Examples

  • The center of mass of a two-particle system lies on the line connecting the particles (or, more precisely, their individual centers of mass). The center of mass is closer to the more massive object.
  • The center of mass of a solid triangle lies on all three medians and therefore at the centroid, which is also the average of the three vertices.
  • The center of mass of a rectangle is at the intersection of the two diagonals.
  • In a spherically symmetric body, the center of mass is at the center. This approximately applies to the Earth: the density varies considerably, but it mainly depends on depth and less on the other two coordinates.

What is the center of gravity?

The center of gravity is the point through which the force of gravity acts on an object. In most mechanic’s problems the gravitational field is assumed to be uniform. The center of gravity is then in exactly the same position as the center of mass. The terms center of gravity and center of mass tend to often be used interchangeably since they are often at the same location. However, they are not the same.

The center of mass of a body does not always coincide with its intuitive geometric center, and one can exploit this freedom. Engineers try to design a sports car’s center of gravity as low as possible to make the car handle better.

Conceded Center of Mass and Center of Gravity (left), Different Center fo Mass and Center of Gravity
Fig. 3: Conceded Center of Mass and Center of Gravity (left), Different Center of Mass and Center of Gravity

The location of the center of gravity can be found by summing the multiplication of the distance by the weight (area) and divide it by the summation of all the weights (areas).

A-Toy-Bird-Balances-When-a-Pivot-is-Placed-at-its-Center-of-Gravity
Fig. 4: A Toy Bird Balances When a Pivot is Placed at its Center of Gravity