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If an object is rigid and not rotating (or threatening to rotate), you may choose an arbitrary location on that object and follow its movement as if it were a point particle. For instance, if you are analyzing a truck moving down the road, you could choose the location of the front axle to specify the truck's position. If you have a non-rigid object or an object that is going to rotate, you still have the freedom to treat the object as a point particle in the 3-D Motion and Momentum and External Force models (and their sub-models) provided you choose to specify the location of the object by the location of its center of mass.
Assumption of a Point Particle in Rotational Dynamics
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