#5 | Conservation of Momentum

(Physics) > Systems of Particles and Rotational Motion

**Conservation of Momentum - Rationale for ignoring internal forces in a system of particles **

Internal forces in a system of particles will exist in pair & will be equal and opposite. (By Newton's third law)

So, in calculation of **acceleration of center of mass**, each pair of internal forces will become zero or cancel each other.

Therefore, internal forces of a system of particles can't impact momentum or acceleration of center of mass. So, they are ignored.

For example: If we consider a system of two particles, any internal force between them such as gravitational, electric or magnetic will not impact momemtum or acceleration of center of mass of above system of two particles.

Please note that coefficient of restitution is defined as (formula 1)

**An equilvalent definition** of coefficient of restitution(formula 2) is based on initial and final kinetic energy of the colliding particles.

Based on values of e, we have to study the following values of e: (though other values of e are possible, they are not in the syllabus)

e = 1 implies **perfectly elastic collion**. (Kinetic enery of the system is conserved based on formula 2 above)

0 < e < 1 implies **inelastic collision**

e = 0 implies **perfectly inelastic collision **(Bodies move together after collision based on formula 1 above)

To solve collision problems, one can use either of the formula 1 or formula 2 with conservation of momemtum equation as both the formulas are equivalent. (Proof for elastic collision is here. Similarly, equivalence of formula 1 and 2 can be proved for inelastic collisions.)

**Always prefer using formula 1(for simpler calculations) along with conservation of momentum to solve problems.**