Race of objects: Three round objects, a hoop, a disk and a sphere, each having radius R and mass M, are at the top of an inclined plane of height h. Their moments of inertia can be written as I = YMR?, where y is a numerical coefficient (which you either know or you can look it up. It is 12 for a disk). The objects are released from the top of an incline with zero initial velocities and they roll down the incline to its bottom, to the finish line. h This round shape is either a sphere, or a disk, or a hoop Finish line VCM a). In this problem, the mechanical energy is conserved, so initial potential energy of an object at the top of the incline must be equal to its total kinetic energy at the bottom. Write an equation based on the conservation of energy for each object and solve it for the velocity of the center of mass Vcm [Recall that in rolling 6 = Vom/R. Use "generic" formula for a moment of inertia yMR? so that your equation will be valid for any of the round objects; at the end you will need to express Vem as a function of h, g, and y (everything else will cancel out) and then substitute values of y for the hoop, disk and sphere and decide in which order they will come down; comment on your reasoning]

b). If the height of the inclined plane is h=1.40 m and its length L = 6.00 m, what will be the time delay At at a finish line between the fastest and the slowest of these three objects? [Hint: you cannot say that t = L/Vcm because Vcm is changing as an object is rolling down; however, you can think in terms of average velocities]