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
Uncertainty of the centripetal force
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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.
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?