Particle, Extended Body, and Rigid Body
How Do Objects Move? From Simple Points to Complex Structures
Think of a ball soaring through the air, a door swinging open, or a suspension bridge bearing the weight of traffic. All of these involve objects in motion - or in equilibrium - but physics doesn’t treat them all the same way. Depending on whether we care about an object’s shape, size, or deformation, we model it as a particle, an extended body, or a rigid body. So what exactly do these terms mean?
The Particle: Physics in Its Simplest Form
A particle is the most stripped-down abstraction of a physical object.
It has mass but no physical size, as if all of its matter were concentrated at a single point in space.
This model is useful when the object’s size is negligible compared to the space it moves through or the scale of the phenomenon we’re analyzing.
For example, a satellite orbiting the Earth can be treated as a particle if we're only interested in computing its trajectory, disregarding its rotation or structural complexity. Of course, the satellite has mass, size, and shape - but if those details don’t affect our analysis, we can simplify it as a point with mass.
Within this framework, we can only describe translational motion - movement from one location to another in space.
Because a particle has no dimensions, it cannot rotate - it has no internal structure to define an axis of rotation.
The Extended Body: When Size and Shape Matter
But in many cases, an object’s dimensions are essential. If we want to understand how an object rotates, flexes, or responds to forces applied at different points, we must treat it as an extended body.
Here, an object’s internal structure can’t be ignored - it plays a critical role in determining how the object behaves under force.
Take a door, for instance: pushing near the handle has a very different effect than pushing close to the hinges.
This is because the impact of a force depends on where it’s applied, and can generate rotation around an axis - a phenomenon captured by the concept of torque, or moment of force, which is the rotational counterpart of force in linear motion.
An extended body is in static equilibrium only when two key conditions are satisfied:
- The net force acting on the body is zero.
- The net torque acting on the body is also zero.
This explains why a table can topple even if it’s not yet moving - too much weight near the edge can produce a torque that tips it over, breaking its equilibrium.
A crucial concept in this context is the center of mass - the effective point at which we consider the object’s weight to act. If that point lies outside the base of support, the object becomes unstable.
Extended bodies can also deform - that is, the distances between points within the object can change under the action of forces.
It's important to remember that these models aren't absolute - they depend on context and the level of precision required. A tennis ball, for instance, can be treated as a particle while it’s in flight, but as an extended body when it bounces or is struck by a racket and begins to deform or spin, altering its trajectory due to the imparted spin.
The Rigid Body: A Useful Idealization
The rigid body is a special case - an extended object that does not deform. Or rather, we assume it doesn’t, for the sake of simplifying the analysis.
In reality, every object deforms to some degree under stress - but in many situations, the deformation is small enough to be ignored.
Unlike a particle, a rigid body has mass, size, and shape, but the distances between all internal points remain fixed, even when forces act on it.
In this sense, the rigid body is a middle ground between the particle and the extended body.
Of course, no real object is perfectly rigid, but this idealization is extremely useful when studying combined motion, such as translation and rotation happening simultaneously.
As with extended bodies, we apply the principles of torque and equilibrium - but the absence of deformation simplifies the math and makes the model easier to work with.
Choosing the Right Model
In physics, picking the appropriate model is the first step to understanding how an object behaves. It all comes down to what you're trying to investigate:
- The particle model is ideal when size and rotation are irrelevant - if you're only tracking translational motion, this abstraction keeps things simple and efficient.
- When the shape, internal structure, or the way forces are distributed matter - like in cases involving bending, rotation, or deformation - you need the extended body.
- The rigid body strikes a practical balance between simplicity and realism. It allows us to study both translation and rotation without dealing with the complexities of deformation.
Ultimately, this is one of the great strengths of physics: the ability to model the world with just the right level of detail for the problem at hand.
As Galileo famously put it, “Nature is written in the language of mathematics.” But to read it clearly… you need the right lens.
