A child swings a rock of mass m in a horizontal circle using a rope of length L. The rock moves at constant speed v.
(a) Ignoring gravity, find the tension in the rope.
(b) Now include gravity (the weight of the rock is no longer negligible, although the weight of the rope still is negligible). What is the tension in the rope? Express the tension in terms of m, g, v, L, and the angle θ that the rope makes with the horizontal.