Physics Tutorial 6.3 - Newton's Second Law for System of Particles Revision Notes

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6.2Newton'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:

  • The definition of particles in physics
  • The role of centre of mass in the dynamics of a system of particles
  • How to write the Newton's Second Law of Motion for a system of particles
  • How to make use of the help of coordinates to study the movement of a system of particles

Newton's Second Law for System of Particles Revision Notes

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

asys = FR(sys)/msys

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

asys = FR1 + FR2 + FR3 + …/m1 + m2 + m3 + …

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:

ax(sys) = FRx(sys)/msys

and

ay(sys) = FRy(sys)/msys

Then, we can use the Pythagorean Theorem to determine the magnitude of acceleration for this system of particles.

asys = √a2x(sys) + a2y(sys)

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