My original teacher in Australia would always start people off doing the "unbendable arm" exercise, allowing them to begin to feel "relaxed power". A similar exercise is the one where you lay flat and imagine you are are a bar of steel while two people lift your head and feet respectively, and your body doesn't bend, despite their being no tension. I gather there may be some kind of scientific explanation for what is going on now.
I do remember an episode of Stan Lee's Superhumans about a man who could make himself magnetic at will and hold a frypan to his head and whatnot. A doctor measured that he had developed what appeared to be an electromagnetic ability through meditation. I imagine that focussing our intent repeatedly during training we develop an ability to move energy through our body in uncommon ways.
I have always noticed that my hands become flushed whenever I "extend ki", a term which I don't use now at all after discovering more fundamental aspects of Aikido that were important, such as developing a good awareness of one's body posture and stance and practicing well-centred movement, as any ability with "ki" is useless without an ability to direct it where it is required.
You'll be learning to move yourself and your training partners through precise curves in space while maintaining complete relaxation, rather like a great penman can draw precisely the right curves on paper* but in a three-dimensional space, intuitively guided by an internal awareness developed over many years.
Did someone say something about ki?
*There are some great Youtube videos on penmanship if you haven't seen it before.