A <cyclic coordinate> is absent from the <Lagrangian> itself: $\partial L/\partial q_i=0$. Its <conjugate momentum> $p_i=\partial L/\partial\dot q_i$ therefore obeys $\dot p_i=0$. In the rolling-wedge calculation, the cyclic horizontal translation gives conservation of the system's horizontal <momentum>.

Solution

Past exam of the physics 1 paper of the University of Oxford / 2019 / 9 / a / i / Solution

 Solution (source code)