A uniform thin rectangular sheet of mass M, width w, and height h can be set into rotation about several different axes that are all perpendicular to the plane of the sheet.
Part labels (a), (b), and (c) refer to the prompts below.
(a) Describe qualitatively how the distribution of mass relative to an axis influences the rotational inertia of a rigid object.
(b) Provide a detailed explanation for why an axis that passes through the center of mass of the sheet must correspond to the smallest possible rotational inertia among all axes perpendicular to the sheet.
(c) Consider two perpendicular axes that both pass through the sheet’s center of mass: Axis 1 is perpendicular to the plane of the sheet, and Axis 2 lies in the plane of the sheet along a symmetry line. Explain whether the rotational inertias about these two axes are the same or different, and justify your conclusion using symmetry arguments.