It is not easy to describe the motion of an object accurately. This is because any object has a certain size and shape, and the motion of their parts is not generally the same. Sometimes we focus on the motion of the parts, and sometimes we focus on the motion of the object as a whole. How to describe an object motion depends on what we are concerned with. In some cases, we can ignore the size and shape of an object and Simplify it to a point without volume and dimension but has mass.
What are the cases the point mass model can be used?
1. When the size or shape of an object has negligible effect on your problem, the object can be considered as a point mass. Although the Earth is very large, its diameter (12,742 km) is less than one ten-thousandth of the Earth-sun distance (about 1.5×10 8 km). Therefore, when the Earth revolves around the Sun, its size becomes a secondary factor and it can be treated as a point mass. In the study of the Earth's rotation, it can not be considered as a point mass.
2. A translating object can be simplifyd to a point mass. Although their sizes and shapes cannot be ignored, the motion of all points is exactly the same. The any point can completely reflect the motion of the whole object. The luggage moves on a horizontal conveyor belt and the metal block slides down the inclined plane.
3. Other than the two cases mentioned above, whether or not to simplify the object to a point mass is determined by your question. Some part of the object is rotating, but we don't consider it in its motion. When a car travels along a road in a straight line, its tires are rotating. The road is not long enough to ignore tires size. If we are only concerned with the displacement, velocity and acceleration of the car, we do not have to consider the rotation of the tires and directly regard the car as a point mass.
A system of particles
When we study the complex object motion, such as rigid body and fluid, although we cannot consider them as point mass, we can think of them as a group of particles. By investigating the motion of these mass points, we are able to solve the whole system's motion.