# Small block on a rotating table

Legaldose
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.

Fc = Ff

and since:

Fc = mv2/r = 4π2rf2m
Ff = μsmg

where v2 = 4π2r2f2

where f is the frequency of rotation in Hz

Now I set

2rf2m = μsmg

2rf2 = μsg

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

r = μsg/4π2f2

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 wanna know if I missed anything or if I have the correct basic intuition behind this type of situation.

Thanks PF! :)

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