The coefficient of restitution (COR) according to some sources (https://en.wikipedia.org/wiki/Coefficient_of_restitution) is equal to the square root of the ratio of final kinetic energy to the initial kinetic energy ?
1) Is this valid in each and every collision?
2) Do we consider the kinetic energy of the two bodies combined or only a single body involved in the collision?
3) In cases involving angular momentum also, should we only consider the translational kinetic energy or the total kinetic energy( translational + rotational) ?
I have tried to derive the COR from the square root of the ratio of final kinetic energy to the initial kinetic energy , but I couldn't solve it completely.
Let us consider the following example.
A particle of mass 1 kg moving with a speed of 20 m/s collides with another particle of same mass but at rest. Let us suppose the speed of the 1st particle becomes 8 m/s without any change in direction and the second particle attains a speed of 12 m/s in the same direction
From COR = speed of separation/speed of approach COR = (12-8)/20 = 1/5 = 0.2
But from COR = final Kinetic energy/initial kinetic energy COR = 0.72
They are not the same which implies one should be wrong or else the example which I have used might not be correct. Help me out with this.