Please provide guidance for the following question.
Which of the following is/are correct?
$1.$ A free particle in $\mathbb R^3$ can have infinite degrees of freedom.
$2.$ The number of degree of freedom of $N$ particles is greater than $3N$.
$3.$ A system of $N$ particles with $k$ constants has $3N+k$ degrees of freedom.
$4.$ A system consisting of three point masses connected by three rigid massless rods has six degrees of freedom.
I think $1$st is wrong, because a particle can have max $3$ degrees of freedom, I would assume in x,y and z direction. Are all of these $3$ degrees translational? Or, one is tranlational, one rotation and one vibration?
Regarding $2$nd, I know that max degrees of freedom of N particles is $3N$, why it is so, I've no idea.
Regarding $3$rd, I am not getting what is meant by $k$ constants.
Regarding $4$th, I checked diatomic example. It has $3$ translational degrees (I assume of co-ordinates), $2$ rotational (I assume clockwise and anti-clockwise), and $1$ vibrational (I assume we have to assume that they are tied by a thread). Similarly, For $3$ particles, I would say, $3$ translational, $2$ rotational and $3$ vibrational (becasue $3$ threads).
I wish somebody could help me see clearly so that I be able to solve this question. Thanks in advance!
