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Block inside a spinning cone  Newton's 2nd Law problem
See attempt at solution. I have attached everything there.
F_net = m * a_n (net force)
W = mg (weight)
a_n = 4*pi^2 * R * f^2 ... formula for "normal" component of acceleration where R = radius, f = rotating frequency
Some questions I have about this problem (look at my work below first or these might not make any sense) 
1. Why is there only a vertical component for the weight? I thought weight always has 2 components whenever an object is on an "incline" which it appears to be here. Does this have something to do with the motion being circular?
2. Why does the normal force have two components if the weight does not? (Ncos(theta) and Nsin(theta))? And further, when exactly do you calculate the normal force or weight using components and when do you not? For example I know on all the incline plane problems I've done, the weight always has two components but normal force is just calculated as N  not using NSin(theta) or NCos(theta).
Basically, in my attempt below, I was just following the method my professor used to solve a similar problem (only difference was his problem had a sphere instead of a block and there was no friction) and I don't really understand why he calculated two above quantities the way he did. I did not get the correct answer so I'm trying to figure this out and having a hard time.
So here's my work:
Homework Statement
See attempt at solution. I have attached everything there.
Homework Equations
F_net = m * a_n (net force)
W = mg (weight)
a_n = 4*pi^2 * R * f^2 ... formula for "normal" component of acceleration where R = radius, f = rotating frequency
The Attempt at a Solution
Some questions I have about this problem (look at my work below first or these might not make any sense) 
1. Why is there only a vertical component for the weight? I thought weight always has 2 components whenever an object is on an "incline" which it appears to be here. Does this have something to do with the motion being circular?
2. Why does the normal force have two components if the weight does not? (Ncos(theta) and Nsin(theta))? And further, when exactly do you calculate the normal force or weight using components and when do you not? For example I know on all the incline plane problems I've done, the weight always has two components but normal force is just calculated as N  not using NSin(theta) or NCos(theta).
Basically, in my attempt below, I was just following the method my professor used to solve a similar problem (only difference was his problem had a sphere instead of a block and there was no friction) and I don't really understand why he calculated two above quantities the way he did. I did not get the correct answer so I'm trying to figure this out and having a hard time.
So here's my work:
Attachments

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