Question

Consider a cylinder of radius R = 1000 km and, for our purposes here, infinite length. Let it rotate about its axis with an angular velocity of Ω = 0.18◦/s. It completes one revolution every 2000 s. This rotation rate leads to an apparent centrifugal acceleration for objects on the interior surface of Ω2 R equal to 1 g. Imagine several competing teams living on the interior of the cylinder, throwing water balloons at each other. (a) Show that when watery projectiles are fired at low speeds (v ≪ Ω R) and low “altitudes” at nearby points (say ∆r ≤ R/10), the equations of motion governing the resulting trajectories are identical to those of a similarly limited projectile on the surface of the Earth. Since this part focuses on low “altitudes”, it makes sense to use a Cartesian coordinate system with z pointed up (i.e. the opposite direction of the effective gravity).

Answer 1