A hoop and a cylinder rolling down a ramp

Explanation:

Mass Distribution: When a hoop and a cylinder of equal mass roll down a ramp with height h, the distribution of mass plays a crucial role in determining the speed at the bottom of the ramp. A hoop has its mass concentrated along the outer edge, while a cylinder has its mass distributed more uniformly around its shape.

Rotational Inertia: The rotational inertia of an object depends on both its mass and how that mass is distributed relative to the axis of rotation. In the case of the hoop, most of its mass is located far away from the axis of rotation, leading to a greater rotational inertia compared to the cylinder.

Energy Conservation: As the hoop and cylinder roll down the ramp, gravitational potential energy is converted into kinetic energy. Since they both start from the same height, the energy is the same for both objects. However, the distribution of mass affects how efficiently this energy is converted into translational motion.

Due to the lower rotational inertia of the cylinder compared to the hoop, the cylinder is able to convert more of its energy into translational kinetic energy, resulting in a greater speed at the bottom of the ramp compared to the hoop. Therefore, the cylinder has a greater speed at the bottom of the ramp.