Central force

Introduction of central force

1. Dr.V.Sharon Samyuktha M.Sc., Ph.D Lecturer in Physics, Maris Stella College, Vijayawada, Andhra Pradesh, India. Experience-13 yrs Research Interest: Ceramics

2. Mechanics and Properties of Matter Course Code: PHYC039

3. CENTRAL FORCES A central force is defined as a force which always acts on a particle or body towards or away from a fixed point and whose magnitude depends upon only on the distance from the fixed point. A central force on an object is a force that is directed along the line joining the object and the origin

4. Central Force on a particle P is expressed by F. Mathematically , F can be expressed as F = r f(r) Where f(r) is a function of the distance r of the particle from the fixed point. r is the unit vector along the radius vector r of the particle with respect to that point.

5. Examples 1. Gravitational force of attraction between two masses

6. 2. The electrostatic force between two charges.

7. Features of Central Forces The general form of central force is given by F = r f(r) Where f(r) is a function of the distance r of the particle from the fixed point and r is the unit vector along the radius vector r of the particle with respect to that point. Central Force is a conservative force. (work done by a force in moving a particle from one point to another is independent of path followed)

8. Under a central force, torque acting on a particle is always zero. Under a central force, the angular momentum of a particle remains constant. The central force is attractive when f(r)<0 i.e., negative. The central force is repulsive when f(r)>0 i.e., positive.

9. Conservation of Angular Momentum According to this law, if no external torque acts on a body rotating about a fixed point, the angular momentum of the boby remains constant. According to definition of torque τ = dL / dt = r X F dL / dt = 0 Integrating we get L = constant

10. Examples of Conservation of Angular Momentum Motion of Planet in its orbit.

11. 2. Scattering of α –particles by a heavy nucleus.