Motion in accel. frames - water in turntable

[aero_zeppelin]

Homework Statement

A small container of water is placed on a carousel inside a
microwave oven, at a radius of 12.0 cm from the center.
The turntable rotates steadily, turning through one revolution
in each 7.25 s. What angle does the water surface
make with the horizontal?

Homework Equations

v = d / t , F = mv^2 / r

The Attempt at a Solution

- We obtain speed from the v equation --> v = 2∏r / t = 0.104 m/s

- Then we use the force equation to obtain --> m 0.0901 m/s^2

- Now we do --> θ = tan^-1 (.0901) / 9.8 = 0.527°

I got this from the book, but my question is: Why are they taking 0.0901 as the y-component and not gravity?! The angle is w.r.t. the horizontal, so the opposite cathetus should be mg...
Centripetal accel. is working on the x-axis and mg on the y-axis, right? So, I don't quite get this...

any help?? Thanks!

 

[gneill]

What's the value of v²/r in the mv²/r formula?

 

[aero_zeppelin]

You obtain v by simply dividing the total distance over time, obtaining v = 0.104 m/s.

- Then from the equation for FORCE CAUSING CENTRIPETAL ACCELERATION:
ƩF = (m)(ac) = (m)(v^2 / r )

You obtain acceleration --> (m) [(0.104 m/s)^2 / 0.12 m ] = 0.0901 m/s^2

And then... you calculate the angle by tan^-1 (y/x) , but that's when I get lost... why are they taking mg as the y component? :(

I'm attaching this MS Paint attempt for the free-body diagram lolll maybe the forces are drawn wrong...

 

[aero_zeppelin]

Ff stands for fictional force and ac stands for centripetal accel btw