Q) A child, Alice, on a playground merry-go-round can be modelled as a point mass m on a homogeneous horizontal disc of mass M and radius a. The disc rotates without friction about a vertical axis through its center. Alice clings to a straight railing that extends from the center of the disc to its perimeter. Alice's distance R(t) from the centre is a function of time determined by her muscles, while the angle θ between the railing and (say) the East is a dynamical variable
Find the Lagrangian for the system. Deduce from Lagrangian that pθ (momentum) is conserved
The disc's (merry-go-round) momentum of inertia is 0.5ma^2
The Attempt at a Solution
In all honesty, I haven't been able to give a serious attempt at this. In lectures we have done no time-dependent examples. Obviously I have to use the formula L=T-V (kinetic - potential energy) however I don't know how I would begin to work out the kinetic energy. Should I start with working out the center of mass?