# Difference between Center of Gravity and Center of Mass

## Main Difference – Center of Gravity vs. Center of Mass

Center of gravity and center of mass are both terms that come up frequently in the study of dynamics in physics. The main difference between center of gravity and center of mass is that the center of mass is defined as the “weighted average” position of mass in a body whereas center of gravity is defined as the point about which the sum of torques due to gravitational forces is 0. For bodies in uniform gravitational fields, the center of gravity and the center of mass are the same.

## What is the Center of Mass

Center of mass is the point in the body or a system of particles where its mass seems to be concentrated. It is found by taking the weighted average position of the mass. Equations used in dynamics are often applicable to the center of mass. When the momentum of a system of particles is computed, the speed of the center of mass is used as the speed of the system. In addition, whenever external forces are applied on a system of many particles or a body, the body behaves as though the external forces were applied at the center of mass. For instance, if you throw a baton up at an angle, the baton may rotate as it falls, however, its center of mass would travel in a parabolic path, as predicted by the equations of motion.

For symmetrical objects with uniform density, the center of mass lies at the geometrical center of the object.

## What is the Center of Gravity

Center of gravity is the point through which all of the weight of the body seems to act. The sum of torques due to gravitational forces is 0 about the center of mass. A body can be balanced by applying a force through the center of gravity. Additionally, if a body is suspended then the center of gravity falls directly below the point of suspension. Center of gravity is also important for stability: a body would topple if its center of gravity is not directly above its base. These rocks maintain their balance because they are skillfully positioned in such a way that the stones’ centers of gravity line up along a single, vertical line.

If a body is in a uniform gravitational field, then it can be shown that the center of gravity and the center of mass coincide. This is approximately the case for objects near the Earth’s surface, whose dimensions are much smaller than the Earth’s radius. However, this is not the case for large objects in space. For instance, if you consider the moon to be a roughly spherical object, the moon’s center of mass is quite close to the geometric center of the “sphere”. However, the side of the moon closer to Earth experiences a stronger gravitational pull compared to the side which is further away. Therefore, the center of gravity is located not at the geometric centre, but on the side closer to Earth.

## What is the difference between Center of Gravity and Center of Mass

### Definition

Center of mass is the weighted average position of mass in a body or a system of particles.

Center of gravity is the point in a body where the net torque due to gravitational forces is 0.

### Dependence on Gravitational Fields

Center of mass does not change when the strength of the gravitational field across a body is varied.

Center of gravity may change when the strength of the gravitational field across a body is varied.

### Position in a Symmetrical Body with Uniform Density

Center of mass is at the geometric center in a symmetrical body with uniform density.

Center of gravity is at the geometric center in a symmetrical body with uniform density, only if the body is in a uniform gravitational field.

### Use in Dynamics

Center of mass is considered to be the point through which all of the mass of a body or a system of particles seem to be concentrated.

Center of gravity is considered to be the point through which the weight of a body seems to act.

Image Courtesy:

“Counter Balance” by Leandro Inocencio (Own work) [CC BY-SA 3.0], via Wikimedia Commons 