Prove that the formula of degrees of freedom is f=3N-K
Answers
The formula for the degree of freedom is 3N-K for a system of particle, it can be proved as -
1. In the formula 3N- K , N and K are the no of particles and no of constraints related to a system respectively.
2. Constraints means no of relation related to a system.
3. For a system the degree of freedom means, how many independent coordinates we need to analyze it.
4. Now, let a three particle system is moving in a space such that distance between them is constant. i.e there is one relation related to distance.
5. To analyze these three particle we need 6 independent coordinates three for each.
6. But there exists one constant distance relation so we need only 5 independent coordinate for that system to be analysed i.e degree of freedom is equal to 5.
7. It can be verified by the formula
by putting N= 2 and K=1. Then ,
DOF= 3×2- 1 = 5.
8. So, It has been verified that the formula for degree of freedom for a system of particles is equal to 3N-K.