This is a question I encountered(for context) : A solid sphere of (radius =R) rolls without slipping in a cylindrical vessel (radius =5R). Find the time period of small of oscillations of the sphere
I tried to solve this by treating it as angular SHM about the center of the cylinder. When I calulate the moment of inertia of the sphere about the centre of the cylinder using the parallel axis theorem and plug it into the equation, I do not get the correct answer. My teacher suggested that since the sphere is not tidally locked, its moment of intertia cannot be appropriately calulated using the parallel axis theorem. I was able to obtain the correct answer from other methods. How to calculate the moment of inertia of the sphere here and how will it differ from the results of the parallel axis theroem.