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An object that has no internal structure, and no physical size. |
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Also commonly called a point mass. |
Motivation for Concept
True point particles do not deform or rotate. In reality, it is basically impossible to find a true classical point particle. Luckily, certain assumptions that allow real (macroscopic) objects to be reasonably analyzed as point particles are often realized in physics problems and in the real world. For example, when a bullet is fired or a fastball is thrown, their rotations are chiefly relevant for their interaction with the air. If air resistance is ignored, the rotation can be as well. Similarly, although all objects deform under the influence of forces, in many cases the deformation is temporary or minor as in the example of pool balls colliding or a rubber ball bouncing off the ground. In such cases the deformation will not significantly affect the symmetries of the object or the dynamics. The deformation can often be reasonably accounted for by treating the object as a point particle but including a correction to the mechanical energy.
Conditions for Treating a Physical Object as a Point Particle
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Assumption of a Point Particle in Linear Kinematics, Momentum and Dynamics
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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. All the problems in kinematics and linear dynamics allow for the specification of the position of macroscopic objects by their center of mass position, and therefore the treatment of these objects as point particles.
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Assumption of a Point Particle in Rotational Dynamics
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If an object is a constituent of a system, it can be treated as a point particle in the Angular Momentum and External Torque model and its sub-models provided that either:
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The first of these two possibilities guarantees that the moment of inertia of the object about the specified axis is completely dominated by Md2 term in the parallel axis theorem. The second possibility implies that the angular momentum of the object about the specified axis can be found using no object variables other than the mass.
Examples of problems in rotational dynamics where one or more constituents of a system are treated as point particles are:
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