Derivation for rotating cylinder

[freeflight1]

The Vertical cylinder vase of radius r is mounted on its center on a
rotator. At rest, it is filled with liquid to a depth of height d. The
vase is then rotated about its vertical axis with angular speed w.
The y axis lies along the rotational axis and the origin of coordinates
is at the base of the vase.

A) Derive the equation that gives the intersection of the liquid
surface with the x-y plane, when dynamic equilibrium is attained at some
w in terms of d,r, and w



B) Find the maximum w for which the bottom of the vase will still be
completely covered with liquid assuming that the bottom is perfectly
flat and that the vase is tall enough to no lose any liquid.

 

We are learning about oscillation and waves right now i really have no idea where to start
i drew this graph I think its right Please help me I dont know where to
start. Please help this is going to be on our exam similer type problem

[daniton]

hi, the first thing what you have to understand is that the velocity of perhaps a unit mass is going to vary depending on the the radius of the unit mass from the axis of rotation.

and the other thing going on is just KE and pressure.you can simply see that the change in KE per unit mass is equal to pressure energy per unit area or change in pressure per unit density(give it a little thought and you will figure out why)

now you have to immediately find the answer to B.Don't for get to use v=w * r for the velocity because there is rotation.

for A just find a general equation of the height reference to lower position of the fluid(it easier reference to this:-)) and the radius.

any ambiguity........

Edited May 9, 2013 by daniton