Central forces are forces that always act toward or away from a fixed point, with a magnitude that depends only on the distance from that point. A central force F on a particle P can be expressed as F = r f(r), where f(r) is a function of the distance r from the fixed point and r is the unit vector along the radius. Examples of central forces include gravitational attraction and electrostatic force. Central forces are conservative, have no torque, and cause angular momentum to remain constant.

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

3. Mechanics and Properties of Matter
Course Code: PHYC039

4. 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

6. • 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.

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

8. 2. The electrostatic force between two
charges.

9. 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)

10. • 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.

11. 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

12. Examples of Conservation of Angular
Momentum
1. Motion of Planet in its orbit.

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