My problem concerns this following figure. This was associated with a practice question. I can solve this properly, but I tend to ask myself things why certain things are the way they are when I go through how to solve it, and I stumbled upon a few questions in my methods.
If I were to resolve the forces on the object in the y - direction, I'd show the following, which I know is fundamentally true. (Referring to the top bit, I can only post 2 links so please bare with me!)
I don't actually, if someone asked me to tell them intuitively, why mgsintheta is opposing the normal force here. It's fundamentally true, as I can show it mathematically, but I can't explain why other than that the normal force is a force that is acting due to gravity on a surface. Because, it could technically be possible for circular motion to happen with just n as the centripetal force as long as it moves at a proportional speed. Also, when solving this, I asked myself "Why can't I call this theta arbitrarily, instead of 90-theta?" If I define their theta as 90-theta, does this equality hold -- could I still solve this accurately, and, if not, why (this refers to the bottom bit!)?