Note that the ribbon tied to the rope moves exactly as did the body around the circle, when it was viewed on edge. It turns out the electrons in their orbits around atomic nuclei exhibit the same behavior. That is, only certain frequencies of oscillation are allowed. There is an energy level associated with each frequency. The higher the frequency, the higher the energy.
Atoms generally absorb and emit energy as quanta , discrete amounts of energy.
For example atoms emit energy, say as light, when one of their electrons lowers its orbit. An incoming photon , or bit of light, can cause an orbiting electron to increase its orbit or its angular momentum. Let's take a look at a video segment that explains all this. Energy levels in between these states are not allowed. Only amounts of energy corresponding to the changes in available states will be emitted or absorbed.