. A. thin rod lies along the x-axis centered and Eli-inert? with a pivot axis at the origin. lts nonuniform linear density is given by HI} = 1.1 {2 _1'1} , with I measured in meters. The rod is llll] cm long and less than 1 cm thick at any point along its length. m Integrate the linear density to nd the total mass Mg of the rod. m 1lllfl'iere is the rod's center of mass Km? You must set up the inte I, but then you may use symmetry arguments to 'ustify your answer if you choose to not evaluate the integral. What is the moment of inertia I; of the rod? mf the rod has an angular velocity ton. = II] radii, what are the rods angular momentum Li: and kinetic energy Kn? Extra Credit: If you cut the rod in half, and threw away the left portion leaving the right half still pegged through the same hole at the origim the mass and the moment of inertia will only ehange by a constant [3, while the center of mass location will change substantially. 'What is the constant ratio [3? Where is the new eenter of mass? Notes: a differential element of mass in 1D is that = Hr] tit. From that you can compute a differential element of moment of inertia in 1D ril' = x2 rim