Are the following equations inversely or directly proportional to frequency?

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SUMMARY

The equation Fc=4π²mrf² illustrates the relationships between frequency (f), radius (r), mass (m), and centripetal force (Fc). Upon rearranging the equation to solve for frequency, it is established that frequency is directly proportional to centripetal force (Fc) and inversely proportional to both mass (m) and radius (r). The square root in the final expression does not alter these proportional relationships. This conclusion clarifies the dependencies of frequency on the other variables in the equation.

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  • Understanding of basic physics concepts, particularly centripetal force.
  • Familiarity with algebraic manipulation of equations.
  • Knowledge of proportional relationships in mathematical equations.
  • Basic understanding of square roots and their effects on values.
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  • Study the principles of centripetal force in circular motion.
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Students studying physics, educators teaching mechanics, and anyone interested in understanding the relationships between frequency, mass, radius, and centripetal force.

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Homework Statement



Re-arrange the equation Fc=4π²mrf² to solve for frequency (f). State the relationship between frequency and (radius, mass, Fc).


Homework Equations


Fc=4π²mrf²


The Attempt at a Solution



Fc=4π²mrf²
\frac{Fc}{4π²mr} = f²
\sqrt{\frac{Fc}{4π²mr}} = f

I have re-arranged the equation though now I need to know the relation between:
•frequency vs radius (r)
•frequency vs mass (m)
•frequency vs Fc (Fc)

Which one is proportional and which ones are inversely proportional? (does the square root affect them)?
 
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\sqrt{\frac{Fc}{4π²mr}} = f

Just forget that there was a square root sign. You'd have Fc / 4n^2 * m * r.
The Square root does reduce the value of the expression inside, but does nothing to the relationships that you are looking for

I have re-arranged the equation though now I need to know the relation between:
•frequency vs radius (r)
•frequency vs mass (m)
•frequency vs Fc (Fc)

If you brought the bottom over, then it becomes clear that Fc is directly proportional to frequency, and that everything else is inversly proportional to frequency.
 
Thank you very much! The square-root was getting to me :) lol.
 

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