In uniform circular motion: When the radius is increased, does the period of rotation increase or decrease?
Depends on what’s happening. Generally the period will increase. See Kepler’s Third Law (the square of the period of rotation is proportional to the cube of the semimajor axis) for orbiting in a central potential (eg gravity). Think of it as the kinetic energy of the particle. In the case of a magnetic field where it doesn’t change its potential energy, it will have the same kinetic energy and so the same speed. But it’s got longer to go, so it’ll take longer to get round. If it’s a central potential like gravity, then it gains potential energy, ie loses kinetic energy as it goes further out. So it slows down and has further to go so it takes longer.
