053 Spring center of mass A uniform spring with a resting length l and a mass M rests horizontally on a table. It is then nth mass anchored at one end and is made to rotate around that end (there is nothing attached to its open nth W(n+ 1)\" end). The act of rotating the spring (and the fact that the spring has mass) causes it to stretch to a Spring Spring new length of L during the rotation. When it is at rest, its center of mass is of course at its center (it is uniform), and it has a rotational inertia equal to what a uniform solid rod of the same length + and mass would have. While it is rotating at this new length, what can be said about its center of E, (x) F;H1(X) mass and its rotational inertia? [Hint: A useful model to use to analyze this is to treat the spring- with-mass as a series of beads-with-mass connected by small massless springs with the same spring constant as the actual physical spring. See the diagram to the right.] L l a. The center of mass is a distance 5 from the pivot, and the rotational inertia equals EMT.2 b. The center of mass is a distance 3 from the pivot, and the rotational inertia is greater than :MLZ. I. 1 ' c. The center of mass is farther than 5 from the pivot, and the rotational inertia equals EMLZ. L d. The center of mass is farther than 5 from the pivot, and the rotational inertia is greater than EMLZ. e. The center of mass is a distance from the pivot, and the rotational inertia equals EMLZ