Answer to last issue's Did You Know? Suppose you have a solid cylinder of wood, and a hoop of iron, both of the same mass and same outer radius. Which of the two will be down first? Ans: We learned in the last issue that a ball of wood and a ball of iron of the same size will reach the bottom at the same time when rolled down a slope. Now the question is about a solid versus a hollow cylinder. Both of them start from the top of the slope at rest, with the same potential energy due to their height h, given by mgh, where m is their (common) mass. As they come down the slope, they lose this energy, which is converted into different forms, according to the law of conservation of energy. Both of them are rolling down the slope, so they have rotational energy. Both are moving downwards so they both have translational energy (technically, their centre of mass is moving down). Hence, the potential enery is going to get converted into translational and rotational energy. For an object to reach the bottom first, it must have maximum speed. To maximize the speed of an object, we must minimise the energy spent in rotation. While they have the same translational energy, their rotational energy depends on their moment of inertia, which indicates how their mass is distributed with respect to their centre of mass. For objects where the mass is further away from the centre, such as in a hoop of iron, where all the mass is concentrated on the outside, the moment of inertia is large. The moment of inertia of a solid cylinder where the mass is uniformly distributed is much smaller. As the moment of inertia decreases, the energy in rotation decreases, so that more of the potential energy is converted into translational energy. Since the solid cylinder has more translational energy, it means that it moves faster and so reaches the bottom first. If you also rolled a sphere along with the hoop and cylinder, you would find the sphere reaches even earlier than the cylinder. Of course, the fastest to reach the bottom would be a solid block (of any material, when friction is ignored) since it has no rotation at all and simply slides down to the bottom.