known and some unknown. Use algebraic symbols for any unknown coordinates or velocities. Note that U includes both gravitational and elastic potential energy, and K includes both translational and rotational kinetic energy. Recall that for an object that rolls without slipping, the speed vcm of the center of mass is given by vcm=r? . SOLVE Write expressions for the total initial mechanical energy and for the total final mechanical energy, equate them, and solve to find whatever unknown quantity is required. REFLECT Take a hard look at your results to see whether they make sense. Are they within the general range of magnitudes you expected? If you change one of the given quantities, do the results change in a way you can predict? SET UP Before writing any equations, organize your information and draw appropriate diagrams. Part A Consider the sketch of the situation described in the problem introduction. What type of velocity does the hoop have in its initial state?What type of velocity does the hoop have in its final state? translational velocity angular velocity zero velocity Enter the letters that correspond to the types of velocities present in the initial state and the letters that correspond to the types of velocities present in the final state of this system separated by a comma. Enter each set of letters in alphabetical order. For example, if the letters A and C represent the types of velocities present in the initial state and A is the type of velocity in the final state, enter AC,A.