Past exam of the physics 1 paper of the University of Oxford / 2014 / 4 / b / Solution

The number of degrees of freedom is the number of independent coordinates needed to specify an allowed configuration locally. For $N$ unconstrained point particles in three dimensions it is $3N$; $k$ independent regular holonomic constraints reduce it to $3N-k$. Redundant constraints must not be counted twice, and nonholonomic velocity restrictions require separate care.