Centripetal Force (RPM Question)

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To determine the maximum RPM a coin can handle on a rotating turntable, the relevant equations include centripetal force, expressed as mv²/r, and the relationship involving the period T, given by 4π²rm/T². The frequency, which is the number of revolutions per second, can be converted to RPM by multiplying by 60. The coefficient of friction of 0.68 plays a crucial role in calculating the maximum speed before the coin slides off. Understanding these equations and their conversions is essential for solving the problem accurately.
McKeavey
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Homework Statement


A coin is placed 18cm from the axis of a rotating turntable of variable speeds. If the coefficient of friction is 0.68, what is the maximum r.p.m that the coin can handle before sliding off?


Homework Equations


This is basically what I need..
I know there's mv^2/r
But which equation do I need for RPM questions?


The Attempt at a Solution


None at the moment, not sure of the equation I'm supposed to use :S
 
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McKeavey said:

Homework Statement


A coin is placed 18cm from the axis of a rotating turntable of variable speeds. If the coefficient of friction is 0.68, what is the maximum r.p.m that the coin can handle before sliding off?


Homework Equations


This is basically what I need..
I know there's mv^2/r
But which equation do I need for RPM questions?


The Attempt at a Solution


None at the moment, not sure of the equation I'm supposed to use :S

As well as mv2/r there is 4∏2rm/T2 where T = period

Since frequency is 1/T that would mean 4∏2rmf2

frequency means revolutions per second. r.p.m is revolutions per minute.
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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