Dynamics Problem: Particle Kinetics - Normal & Tangential Components - Problem1 (Gravitron Problem)

Without a doubt you'll see at least one of these types of problems in your Dynamics class. It involves an object being spun in a circle at a great enough speed such that the static friction force is able to hold it in place and prevent it from sliding down (or up).
This is the working principle of the "Gravitron" carnival ride
Gravitron: en.wikipedia.org/wiki/Gravitron

[@fallofmanbrand]

great video you deserve more views

[@marcelofarfan5312]

For the forces we got for the x -axis, I get we made them positive cause of how we set up our axis. But, would there be any consequences though if we had set it were arrows pointing to the left were negative?