Rigid System
Also called Rigid body
A rigid system is a system that does not change shape, but whose different points may move in different directions and with different speeds. It is the model AP Physics uses whenever rotation matters and the object model is no longer enough.
College Board defines it in that wording, in the appendix Vocabulary and Definitions of Important Ideas in AP Physics. The appendix's example is a wheel on a horizontal axle. As it turns, every point keeps its place relative to every other point, so the shape never changes, yet a point near the rim travels faster and in a different direction than a point nearer the hub at the same instant.
That difference is what the object model cannot hold. An object has no size, so it has no near-the-rim and no near-the-hub. The moment the rotation is relevant to the analysis, the appendix says, the wheel has to be modeled as a rigid system instead.
Where the force is applied now matters. For a rigid system, pushing the top of the wheel does something different from pushing the bottom, and different again from pushing straight at the axle. This is why AP Physics 1 introduces force diagrams alongside free-body diagrams in Topic 5.3: EK 5.3.B.1.ii says force diagrams also depict the location at which the forces are exerted relative to the axis of rotation.
The phrase is not decoration. It is the noun the rotational learning objectives actually use, so the exam asks you to identify the torques exerted on a rigid system (LO 5.3.A) and to describe a rigid system's rotational inertia relative to a given axis (LO 5.4.A). EK 5.4.B.1 adds that a rigid system's rotational inertia in a given plane is smallest when the axis passes through its center of mass.