Small block on a rotating table

  • Thread starter Legaldose
  • Start date
  • #1
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Main Question or Discussion Point

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! :)
 
Last edited:

Answers and Replies

  • #2
Well technically the object does matter since you will get different frictional coefficients depending on the materials you end up putting on the table. But yea, if you can get the same frictional coefficients then they would be the same.
 
  • #3
74
6
Yea I forgot to include the friction coefficient in that sentence, oh well D:
 

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