1. The problem statement, all variables and given/known data A massless hoop is suspended horizontally and is free to rotate about a vertical axis through its center with a constant angular velocity (omega). Attached to the edge of the hoop is a simple pendulum that is restricted to oscillate in only the radial direction. find the Lagrangian of the system. M= mass of pendulum L= Length of Pendulum ∅= angle the pendulum makes with the vertical ω=angular velocity of hoop R= radius of hoop 2. Relevant equations L= T-U T= Kinetic energy U=Potential Energy 3. The attempt at a solution T(hoop)=(1/2) I(hoop)*ω^2 But I is dependent upon the mass of the hoop and since the mass of the hoop is 0 so is I(hoop)->T(hoop)=0 T(pendulum)=(1/2)M[L*(d∅/dt)]^2+(1/2)I(pendulum)*ω^2 T=1/2M[(L*d∅/dt)^2+(R+Lsin∅)^2*ω^2 U=-MgLcos∅ L=(1/2M[(L*d∅/dt)^2+(R+Lsin∅)^2*ω^2)+MgLcos∅ Is this right?