Introduction to Classical Mechanics · Problem 3.24
Using F = ma — Morin
Physics — Mechanics · free_particle_polar
Problem
Free particle ***
Consider a free particle in a plane. With Cartesian coordinates, it is easy to use F=ma to show that the particle moves in a straight line. The task of this problem is to demonstrate this result in a much more cumbersome way, using polar coordinates and Eq. (3.51). More precisely, show that cosθ=r0/r for a free particle, where r0 is the radius at closest approach to the origin, and θ is measured with respect to this radius.