What is the difference between centre of mass and centre of gravity?

Answer

To understand the difference between the center of mass and the center of gravity, we can break it down into a few key points:

### Step 1: Definition of Center of Mass
The center of mass (COM) of an object is defined as the point at which the mass of the object can be considered to be concentrated for the purpose of analyzing translational motion. It is the average position of all the mass in the object and is determined solely by the distribution of mass within the object.

### Step 2: Definition of Center of Gravity
The center of gravity (COG) is the point at which the weight of an object is balanced. It is the point where the total weight of the object can be considered to act. The center of gravity depends on the gravitational field acting on the object, as it is the weighted average of the distribution of mass, taking into account the gravitational force (weight = mass × gravitational acceleration).

### Step 3: Dependence on Gravitational Field
The center of mass is independent of the gravitational field; it is a geometric property of the object. In contrast, the center of gravity is dependent on the gravitational field because it considers the weight of the object, which varies with different gravitational fields.

### Step 4: Application in Different Gravitational Fields
In a uniform gravitational field (like near the surface of the Earth), the center of mass and center of gravity coincide and are at the same point. However, in a non-uniform gravitational field, the center of gravity may not coincide with the center of mass due to varying gravitational forces acting on different parts of the object.

### Summary of Differences
1. **Definition**: COM is based on mass distribution; COG is based on weight distribution.
2. **Dependence**: COM is independent of gravity; COG depends on the gravitational field.
3. **Location**: In uniform fields, they coincide; in non-uniform fields, they can differ.