Point Mass

Also called Point object

A point mass is a body idealized as all of its mass concentrated at a single location, with no size and no shape. It is what AP Physics means when it says an object may be treated as a single point.

AP Physics 1 EK 1.2.A.1 puts it directly: when using the object model, the size, shape and internal configuration are ignored, and the object may be treated as a single point with extensive properties such as mass and charge. That single point is the point mass.

Two places where the idealization does visible work:

Rotational inertia. EK 5.4.A.2 gives $I = mr^2$ for an object rotating a perpendicular distance $r$ from an axis, and EK 5.4.A.3 sums those to $I_{tot} = \sum m_i r_i^2$ for a collection. Both formulas need each mass to sit at one definite distance, which only a point mass does.
The simple pendulum. AP Physics C: Mechanics EK 7.5.A.3 describes it as the special case of a physical pendulum in which the hanging object can be modeled as a point mass at a distance $l$ from the pivot.

A whole system can be reduced to a point mass at its center of mass whenever its internal structure does not matter. The moment it does matter, as when a wheel's rim and hub move at different speeds, the model has to become a rigid system instead.

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