# Intuition behind physics of a circular ramp

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!)?

• Have you tried to solve it that way? Do you have any real reason to think you can't? – JMac May 4 '17 at 21:02
• All that happens when you use $\phi = 90-\theta$ is that a $\sin \theta$ might become a $\cos\phi$, etc. Apart from that, the laws of physics don't change just because you change your coordinate system. – Floris May 4 '17 at 21:21
• I actually just realized I forgot to mention my other question. 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. – sangstar May 4 '17 at 23:34