What is the mathematical proportionality for centripetal acceleration?

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SUMMARY

The discussion focuses on determining the mathematical proportionality for centripetal acceleration using the formula UgM = 4π²rm/T². Participants derived empirical relationships indicating that T is proportional to M^-0.35, m^0.53, and r^0.5. The final expression combining these relationships is T = Constant * M^-0.35 * m^0.53 * r^0.5, where the constant can be deduced from logarithmic graph intercepts. The derived relationships show slight discrepancies from the original formula but remain closely aligned.

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bayan
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Hi everyone!

We have been doing a n experiment about Cent acceleration.

We had a formula which was UgM= 4Pie^2rm/T^2

Then we have T being ptoportional to M, R and m

Can someone help me to figure out the proportionality?

It is to be determined using maths although I have got some result (not using maths, only from our observation of graphs and making the LOG graph to find gradiant..) I have got it to be
T proportional to M^-.35
T proportional to m^.53
T proportional to r^.5


Is there anyone that can help me to fing what the mathematical proportionality would be?

Also any work out would be apriciated to explain.
 
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Your plotted data has given you empirical exponents for the dependence of T on each of three variables. I assume your data was collected by allowing only one of the three to vary at any time. When you say "T proportional to M^-.35" You are saying T is some constant times M^-.35, but that constant may depend on the other two variables that you are holding fixed. Similar reasoning appplies to the other two variables. Putting them all together gives you

T = Constant*M^-.35*m^.53*r^.5

The value of the constant can be deduced from the intercepts of logarithmic graphs you plotted.

Your data does not quite agree with your starting formula, but it is not terribly far off.
 

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