There is a certain fundamental feeling that comes alongside doing physics (particularly theoretical) which is unexpectedly heady and exhilarating - a feeling that you would never expect to experience when doing simple mathematical calculations.
The feeling of physics is when you can predict the future. Without performing any such investigation, predicting the motion of a pendulum, falling body or accelerating car. Predict exactly what would happen if the car impacted the pendulum, where the energy would go and what would happen to both. Scaling up, this can be used to predict the motion of the sun, stars and planets - the motion of the lunar lander and rockets launching at this very moment. We can predict phenomenon that we will never see and can never hope to see. We can predict anything about the future, given enough time and enough information about the present
The feeling of physics is being able to prove and know the existence of particles and concepts too microscopic for us to ever hope to see them, and yet to, nevertheless, understand them better than we could ever hope to otherwise. We can deal with immense quantities of energy, that which we will never use in a lifetime, and yet we can deal with the most miniscule of details so small that the number of them defies our understanding of numbers. We can know of theoretical concepts that could never possibly have a grounding in practicality, and yet which are logically sound when investigated. The feeling of physics is reading about things which you can never even hope to see, and yet which you can be confident are all around you as you speak.
The feeling of physics is the ability to think on paper and to see your paper map out into reality, as what you have on paper is reality. Predictions of the movement of a space craft, the sun or even a baseball which proceed to follow your command to the very last detail. Design of buildings, machines or mechanisms which work on paper we can be confident will work in reality too. The feeling of physics is the ability to express immensely complex ideas with algebra and numbers. The motion of planets, coiling of springs and the movement of particles - all expressed using π, equations and simple multiplication. By solving for x, we can solve for the secrets to the universe.
The feeling of physics is to be transported to the center of the sun, edge of a black hole or distant galaxies terametres away all while sat in a laboratory or in school. We can see things that no human alive will ever see, like the core of a nuclear reactor, the planet or a thermal explosion. The knowledge that the concepts that seem so alien to us, concepts that couldn’t possibly be true are actually happening, in reality - right now, as we speak. The amazement felt as you realise that this enormous fantasy you have seemingly been taught is, in fact, very real and in the same world as you are.
The feeling of physics is to be able to look out at the crescent moon from your window and marvel at the beauty - not just of the moon itself, but also of the fact that we have the power to figure out (using simple optics and pi) what exactly is going on on the surface of the moon right now. And so, as I sit writing this staring at the moon, I can know that I know what is happening 238,855 miles away from me on that giant orb in the sky we call the moon.
All of this is the feeling of physics.