How Does Water Angle in a Rotating Carousel Microwave?

[metallica007]

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 revolu-
tion in each 7.25 s. What angle does the water surface
make with the horizontal?

Homework Equations

F=ma
a=v^2/r
v=(2pi*r)/t

The Attempt at a Solution

The problem is very challenging for me that I did not know how to start think about it!

Note: I attached the solution, could you please explain it to me

 

[ashishsinghal]

Hey Metallica007,
Frankly, I did not clearly understand their solution and so I will give my attempt at it:

Consider a small volume of water in the container. Let it be a horizontally kept cylinder. Let its area be a and length be l. Since the surface is inclined both the faces of the cylinder would not have equal height of water above them. Hence they have a difference in pressure and hence force on both sides. Equate this difference to the required centripetal force. You will get the value of h/l. This is equal to the tan of the angle.

 

[ashishsinghal]

But the angle will change as you go away from the center but not in this case. Because they have given you that the container is small.

 

[tiny-tim]

hi metallica007!

(have a pi: π and try using the X² icon just above the Reply box )

the answer is using a https://www.physicsforums.com/library.php?do=view_item&itemid=87" of reference …

ie, you imagine that you're rotating with the turntable: then Newton's laws all work provided you add a "fictitious" force, the https://www.physicsforums.com/library.php?do=view_item&itemid=84" …

so you include that centripetal force on the LHS of F_total = 0

(if you don't use a rotating frame, you get the same result by putting https://www.physicsforums.com/library.php?do=view_item&itemid=27" on the RHS of F_total = ma )