Use calculus to prove that the center of mass of uniform thin rod is located at the geometric center of the rod_ [10] (b) A thin rod of length 2 m has linear mass density A() kgm where % is a dimen- sionless quantity representing length: Using calculus find the moment of inertia (I2) of the rod about an axis (Z) that is perpendicular to the rod and passes through the point where 03 [10] (c) Suppose now that the rod mentioned in part (b) is rotating with a constant angular velocity S 1 around Z axis. Using calculus determine the kinetic energy (K) of the rod [10] (d Use the results of parts and (c to verify that the relation K = %Iz? holds. [2]