# Why do we say linear molecules only have 2 rotational degrees of freedom? Why does the third 'frozen' one not count?

The number of degrees of freedom isn't $3N$, it's $3N$ minus the number of contraints.

The $N=2$ is a special case since with two particles molecules can't help being linear. However for $N>2$ if the molecule is linear you are constraining the motion of the third particle because it can only move along the line joining the other two. Likewise for higher values of $N$. This reduces the total number number of degrees of freedom, so the transaltional, rotational and vibrational degrees of freedom do not have to add up to $3N$.