Definition, examples and features of Central Forces

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.