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a small ball is placed inside a larger hollow ball, which is spun at a frequency of "f" around an axis passing through the centre(axis from 12 oclock position to 6) there is no notable friction. what is the height "h" that the small ball will rise to inside the large one.

use r,f,g to define the height

http://picasaweb.google.com/devanlevin/DropBox?authkey=sbH95pBl_D8#5273423507587078018 [Broken]

excuse my artwork

what i did was:

defined the height==> h=r-rcos[tex]\alpha[/tex]=r(1-cos[tex]\alpha[/tex])

define the velocity==>v=2[tex]\Pi[/tex]r*f

broke the vectors into radial and tangential components, then said

[tex]\sum[/tex]F(radial)=N-mgcos[tex]\alpha[/tex]=m[tex]\frac{v^{2}}{r}[/tex]

N-mgcos[tex]\alpha[/tex]=mr(2[tex]\Pi[/tex]f)[tex]^{2}[/tex]

cos(alpha)=N/mg - (r/g)(2pi*f)^2

h=r(1-=(N-mr(2[tex]\Pi[/tex]f)^2)/mg)

is this correct up to here?

now the part im not sure of at all,

how to get rid of N?

the correct answer is

h=r(1-g/(r(2pi*f)^2)

when f>(1/2pi)*sqrt(g/r)

and h=0

when f<(1/2pi)*sqrt(g/r)

how do i get these conditions, and where have i gone wrong finding the expression for h

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# Maximum height

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