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In addition to the revision notes for Newton's Second Law for System of Particles on this page, you can also access the following Centre of Mass and Linear Momentum learning resources for Newton's Second Law for System of Particles
|6.2||Newton's Second Law for System of Particles|
In these revision notes for Newton's Second Law for System of Particles, we cover the following key points:
In physics, particles are objects whose dimensions are very small compared to their motion. Therefore, we do not consider the shape of particles at all during the calculation process and as a result, the study of their centre of mass gives the same result as the study of the entire system of particles.
All objects move because of the action of any force. Therefore, if there is any motion of a certain object, there is a force acting on the object as well. Thus, when a system moves, we can apply the Newton's Second law of Motion, which outlines the relationship between acceleration, acting force and mass of an object.
The same thing can be said for a system of particles as well. We must only replace the mass of a single object by the mass of the entire system and the force acting on a single object (or better, the resultant force) with the resultant force acting on all particles of the system. Then, the equation
is used to determine the acceleration of the entire system.
The extended Equation of the Newton's Second Law of Motion for a system of particles is
where 1, 2, 3, are the indexes for the objects included in the system.
When written in coordinates, the above equation (which is in vector form), splits in two (or three) similar equations written for each dimension separately:
Then, we can use the Pythagorean Theorem to determine the magnitude of acceleration for this system of particles.
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