Here is a case where we have vertical circular motion, a pendulum or swing, where it is a bit more complicated than horizontal circular motion. For a pendulum, the tension and gravity components vary with the angle, so we have non-constant forces and acceleration. This could be tough to solve with Newton's laws. However, with energy we can find speeds more easily, and this will allow us to find the tension in the string for any angle of its motion. Check it out.