1. The problem statement, all variables and given/known data Consider a uniform semicircular disk of radius R, which rolls without slipping on a horizontal surface. Recall that the kinetic energy of an object is the sum of the translational kinetic energy of the centre of mass (point C) and the rotational kinetic energy about the Centre of Mass. Using Lagrangian methods, show that the angular frequency of small oscillations is ω = sqrt([8g]/[R(9π -16)]) 2. Relevant equations .5mR2 = Ic + mh2 where h = 4R/3π L = K - U dL/dq = (d/dt)(dL/dq') 3. The attempt at a solution First thing to do is find the center of mass of the object so i solved for that to get (x,y) = (o, 4R/3π) Then using that I solved for the moment which equals .5mR2 Using the parallel axis thheorem i found that .5mR2 - mh2 = Ic K = .5mv2 + .5Ic2 U = mghcos(∅) ( i think) This has no R dependance so the Euler Lagrange only acts on theta and omega problem is it's not work, so i obviously messed up on my kinetic and potential energies.