11) A solid sphere, a uniform disk, and a hollow hoop all having identical masses and radii are started from rest at the top of an inclined plane simultaneously. The sphere reaches the bottom first. Using Newton's Laws and rotational dynamics show why this must be true. (Hint: Draw a FBD showing the forces present, and determine which are responsible for translation and which for rotation. I for the hoop = MR², I for the disk is 1/2MR² and I for the solid sphere is 2/5MR². Base you answer on the acceleration of the center of masses of each object.)

11) A solid sphere, a uniform disk, and a hollow hoop all having identical masses and radii are started from rest at the top of an inclined plane simultaneously. The sphere reaches the bottom first. Using Newton's Laws and rotational dynamics show why this must be true. (Hint: Draw a FBD showing the forces present, and determine which are responsible for translation and which for rotation. I for the hoop = MR², I for the disk is 1/2MR² and I for the solid sphere is 2/5MR². Base you answer on the acceleration of the center of masses of each object.)