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Mechanics by Somnath Datta

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Chapter 9

Motion Under Central Forces

Central forces enjoy a special place in physics. The most prominent forces in nature, namely, the force of gravitation between two spherically symmtric massive bodies (e.g., a star and its planet) and the electrostatic force (Coulomb force) between two point charges in slow motion 1 are central forces.

By the term “central force” we mean a force F(r) acting on a particle P which is (a) always along the line CP joining P to some centre C (Fig. 9.1a), and which is (b) a function only of the radial distance r measured fron the centre C. The function F(r) is independent of the angle θ that the radius vector r makes with some arbitray direction in space.

 

 

FIGURE 9.1 Examples of a central force: (a) A schematic ...

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