A force Fθ = 2mr˙θ˙
Consider a particle that feels an angular force only, of the form Fθ = 2mr˙θ˙. Show that r = Aeθ + Be−θ, where A and B are constants of integration, determined by the initial conditions. (This force is actually a physical one. If you put a bead on a stick and swing the stick around one end at a constant rate, then the normal force from the stick happens to be 2mr˙θ˙.26)