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# Uncertainty of the centripetal force

A lab experiment was performed to find the centripetal force on a rotating body which measured mass(m), frequency(n), and radius(r).  It was found that Fc=4Π2n2mr.  How do I write an expression for the uncertainty of the centripetal force?  Thank you

### 2 Answers by Expert Tutors

Andre W. | Friendly tutor for ALL math and physics coursesFriendly tutor for ALL math and physics ...
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Let δn, δm, and δr be the uncertainties of n, m, and r, respectively. Then the error propagation law tells us that the relative uncertainty of the product F=4Π2n2mr is

δF/F = 2 δn/n + δm/m + δr/r,

from which you can find δF.
Note: a constant factor (4Π2) does not contribute to the relative uncertainty, whereas the exponent 2 in n² becomes a factor of 2 in the relative uncertainty.

Alternatively, you can compute the total differential of F,

dF = (∂F/∂n) dn + (∂F/∂m) dm + (∂F/∂r) dr
= (8Π2nmr) dn + (4Π2n2r) dm + (4Π2n2m) dr.
Steve S. | Tutoring in Precalculus, Trig, and Differential CalculusTutoring in Precalculus, Trig, and Diffe...
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Wouldn't you just convert to differentials?

dF = 4pi^2 (dn)^2 (dm) (dr)

where each differential would be replaced with the uncertainty of that value?