Modeling in physics depends on what details matter. Many real systems have parts that respond differently, and the “right” system model can change as external conditions change during motion.

Internal structure: when “one object” is not enough

A system can contain multiple objects or multiple parts of one object. The internal structure is the set of components and constraints (contacts, links, couplings) that determine how those parts move relative to each other.

When internal structure matters, treating everything as a single object can hide important behavior:

• Different parts can have different accelerations (non-rigid behavior).

• Parts can store or release energy internally (deformation, compression).

• Connections can transmit forces imperfectly or fail.

A practical goal is to choose the simplest model that still matches the observed motion.

Subsystems and why we redefine them

Often you analyze a complex system by dividing it into subsystems whose interactions you track explicitly.

Two free-body diagrams for a two-block system on an incline, isolating block A and block B separately. The contact forces (normal and friction) appear as external forces on each isolated subsystem, making the across-boundary interactions explicit. This helps students see how subsystem boundaries control which forces show up in each diagram. Source

Subsystem choices are not unique. You pick boundaries to make the physics transparent:

• Separate parts when they can move differently.

• Combine parts when they move together in a predictable way.

• Redraw subsystem boundaries if the physical connections or constraints change.

How external variables can change substructure

The syllabus emphasis is that changing external variables can change the system’s substructure. Here, “external variables” means conditions imposed by the environment, such as:

• The magnitude or direction of an applied push/pull

• The angle or motion of a supporting surface

• The speed of the system through a medium

• Whether a constraint is present (a barrier, latch, or guide)

These changes can alter which components effectively act together.

An object on an incline with the weight vector decomposed into components parallel and perpendicular to the surface. This visual reinforces why a change in an external variable (the incline angle) changes the force components you use, while the normal force remains perpendicular to the surface. It supports setting up Newton’s 2nd law along axes aligned with the surface. Source

Common substructure changes to watch for

• Contact begins or ends: an object lifts off, collides, or loses contact with a surface.

• Coupling switches state: parts that were “locked together” begin to slip, separate, or hinge.

• Constraint activates/deactivates: a rope goes taut after slack, a stop is reached, or a latch engages/disengages.

• Internal deformation becomes relevant: a “rigid” approximation fails when bending or compression affects motion.

In each case, the system is the same physical collection of matter, but your model’s internal connections (and therefore the best subsystem breakdown) changes.

What changes in your diagrams and equations

When the internal structure changes, your analysis must update in three coordinated ways.

1) Update the object list and boundaries

• If two parts move together: you may combine them into one subsystem.

• If they begin moving differently: split into separate subsystems.

• If a connector breaks or releases: remove that interaction from the model after the change.

2) Reclassify forces as internal vs across-boundary

Forces between parts inside the chosen system boundary are internal; forces from outside are external to that system (or subsystem). If you redraw subsystem boundaries, some forces change category:

• A contact force between two blocks is internal to the two-block system

• The same contact force is external to either block subsystem

3) Rebuild the interaction representation

When substructure changes, the set of interactions changes:

A free-body diagram for motion on an inclined surface, labeling the normal force $N$, friction $f$, and weight $w$. The figure emphasizes that the relevant force components depend on the chosen axes (parallel/perpendicular to the incline), which is a common reason students must rebuild equations when conditions change. It also highlights which interactions are present (contact and friction) versus absent. Source

• A lost contact means a contact interaction is removed.

• A newly engaged constraint means a new interaction is added.

• A “together” model may replace multiple interaction forces with a single effective external influence on the combined subsystem.

Careful language helps: you are not changing the physics, you are changing which interactions you treat as inside the model versus imposed from the environment.

Signs your subsystem model must change

Look for these indicators:

• One part’s motion stops matching another part’s motion (relative slipping, separation, or rotation).

• A connector reaches a limit (fully stretched, fully compressed, or hits a stop).

• The environment condition changes abruptly (surface ends, support angle changes, external agent lets go).

• Predictions become inconsistent (a required internal force would exceed what the connection can provide).