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Imagine a surface that rotates with frequency f about its center, if we set a small block (or a coin, or any flat object for that matter) on the table, I wanted to calculate the maximum radius that you can place this block from the center before it starts to move outward from the center. This is how I did it:

I figured the maximum centripetal force on block had to equal the maximum frictional force keeping it in place.

and since:

where

where f is the frequency of rotation in Hz

Now I set

The mass variables m cancel, this is why we can add any object, as long as it's center of mass rests at a distance r from the center.

Now it's easy to see that

I think it's interesting that the distance is

Would this be considered a correct derivation? Basically I just want to know if I missed anything or if I have the correct basic intuition behind this type of situation.

Thanks PF! :)

I figured the maximum centripetal force on block had to equal the maximum frictional force keeping it in place.

**F**_{c}= F_{f}and since:

**F**

F_{c}= mv^{2}/r = 4π^{2}rf^{2}mF

_{f}= μ_{s}mgwhere

**v**^{2}= 4π^{2}r^{2}f^{2}where f is the frequency of rotation in Hz

Now I set

**4π**^{2}rf^{2}m = μ_{s}mg**4π**^{2}rf^{2}= μ_{s}gThe mass variables m cancel, this is why we can add any object, as long as it's center of mass rests at a distance r from the center.

Now it's easy to see that

**r = μ**_{s}g/4π^{2}f^{2}I think it's interesting that the distance is

__only__dependent on how fast the table is rotating, and that there are no other factors(other than what planet you are on :p) that determine it.Would this be considered a correct derivation? Basically I just want to know if I missed anything or if I have the correct basic intuition behind this type of situation.

Thanks PF! :)

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