Racing a Hoop, a Disk, and a Sphere - oh my!


Three objects have the same mass, and the same radii : a hoop, a disk, and a sphere. They are all at the same place at the top of an incline as shown (you are only seeing the one closest to you at the moment). When you run the animation, the three masses are released, and they roll, without slipping, down the incline. Your task is to figure out the color of each object (each object above is shown as a circle of a particular color). Mathematically prove your answers by calculating the acceleration of each object down the incline. [Hint, use the energy equation and the v2 kinematics equation.] The vertical height of the incline is 1 meter, and the distance along the incline is 2 meters (thus, it is a 30 degree angle for the incline).