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Center of mass - Motion of the center of mass

Center of mass - Motion of the center of mass: Encyclopedia II - Center of mass - Motion of the center of mass

The following equations of motion assume that there is a system of particles governed by internal and external forces. An internal force is a force caused by the interaction of the particles within the system. An external force is a force that originates from outside the system, and acts on one or more particles within the system. The external force need not be due to a uniform field. For any system with no external forces, the center of mass moves with constant velocity. This applies for all systems with classical internal forces, in ...

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Center of mass, Center of mass - Aeronautical significance, Center of mass - Animations, Center of mass - Barycenter, Center of mass - Comparison with center of gravity, Center of mass - Definition, Center of mass - Example, Center of mass - Examples, Center of mass - More formulas, Center of mass - Motion of the center of mass, Center of gravity, Centroid, Pappus's centroid theorem, Center of pressure

Center of mass: Encyclopedia II - Center of mass - Motion of the center of mass

Center of mass - Motion of the center of mass

For any system with no external forces, the center of mass moves with constant velocity. This applies for all systems with classical internal forces, including magnetic fields, electric fields, chemical reactions, and so on. More formally, this is true for any internal forces that satisfy the weak form of Newton's Third Law.

The total momentum for any system of particles is given by

Where M indicates the total mass, and v_cm is the velocity of the center of mass. This velocity can be computed by taking the time derivative of the position of the center of mass.

An analogue to the famous Newton's Second Law is

Where F indicates the sum of all external forces on the system, and a_cm indicates the acceleration of the center of mass.

The angular momentum vector for a system is equal to the angular momentum of all the particles around the center of mass, plus the angular momentum of the center of mass, as if it were a single particle of mass M:

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Adapted from the Wikipedia article "Motion of the center of mass", under the G.N U Free Docmentation License. Please also see http://en.wikipedia.org/wiki

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