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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.

enter image description here

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!)

enter image description here

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!)?

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    $\begingroup$ Have you tried to solve it that way? Do you have any real reason to think you can't? $\endgroup$ – JMac May 4 '17 at 21:02
  • $\begingroup$ 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. $\endgroup$ – Floris May 4 '17 at 21:21
  • $\begingroup$ 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. $\endgroup$ – sangstar May 4 '17 at 23:34

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