# When to Consider a Body as a Point-Like Object: Factors and Applications

• MathematicalPhysicist
In summary, when considering a three-dimensional body as a point-like body in calculations, it is typically done outside of theoretical or homework practices. This is usually when the geometric properties of the body are not important and can be ignored in the calculations. Another reason could be if the body is a particle. This simplification can make it easier or possible to solve the problem. This concept is also used in other fields, such as treating pool balls as mathematical points rather than spherical objects in order to make calculations easier.
MathematicalPhysicist
Gold Member
my question is as follows:
when do we need to consider a three dimension body as a point like body in our calclulations?
i mean outside our theoretical/homework practices when should we assume the body as a point like?

one thing i can think of is when the geometric properties of a body is not important and therefore isn't taken into consideration into our calculations.
and maybe also when the body is a particle but other than that i don't know.

When it makes it easier or possible to solve the problem.

loop quantum gravity said:
my question is as follows:
when do we need to consider a three dimension body as a point like body in our calclulations?
i mean outside our theoretical/homework practices when should we assume the body as a point like?

one thing i can think of is when the geometric properties of a body is not important and therefore isn't taken into consideration into our calculations.
and maybe also when the body is a particle but other than that i don't know.

We can treat the Newtonian gravitational field (GM/r^2) of a spherically symmetric body as if the body were a point.

The center of mass is a useful concept for the motion of rigid bodies as well. If we apply a force to a rigid body, we know that the acceleration of the center of mass is F/m.

I don't do much in the way of science other than haunting these premises. My experience with your question actually is the basis of how I play and teach pool. When calculating how to hit a ball, I treat each one as a mathematical point rather than a spherical object. I then envision what angle to fire a laser at in order to achieve the proper 'reflection', followed by extrapolating the radii in order to accommodate the edge-to-edge contact of the balls.

Danger said:
I don't do much in the way of science other than haunting these premises. My experience with your question actually is the basis of how I play and teach pool. When calculating how to hit a ball, I treat each one as a mathematical point rather than a spherical object. I then envision what angle to fire a laser at in order to achieve the proper 'reflection', followed by extrapolating the radii in order to accommodate the edge-to-edge contact of the balls.
and ofcourse you always lose...

loop quantum gravity said:
and ofcourse you always lose...
Oooh... you sting me! (Wanna play for \$? )

## 1. What is a point-like object?

A point-like object is an object that can be treated as a single point in space, meaning it has no significant size or shape and its location can be described using only its coordinates.

## 2. What factors determine whether a body can be considered as a point-like object?

The size, shape, and distribution of mass of the body are the main factors that determine whether it can be treated as a point-like object. Other factors such as the distance of observation and the precision of measurement also play a role.

## 3. When is it appropriate to consider a body as a point-like object?

In general, a body can be considered as a point-like object if its size is significantly smaller than the distance at which it is being observed, and if its shape and mass distribution do not significantly affect its motion or behavior.

## 4. What are some applications of treating a body as a point-like object?

Treating a body as a point-like object is often used in physics and engineering calculations, such as in the study of motion and forces, as well as in the design of structures and machines. It is also commonly used in astronomy and astrophysics to simplify calculations and models of celestial bodies.

## 5. Are there any limitations to treating a body as a point-like object?

Yes, there are some limitations to treating a body as a point-like object. For example, in some cases, the shape and mass distribution of a body may significantly affect its behavior, and thus cannot be ignored. Additionally, treating a body as a point-like object may not be accurate for very precise measurements or in situations where the size of the body is not negligible compared to the distance at which it is being observed.

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