Question #aa46e

In the classical sense , the centripetal force #F# can be measured as:

#F = (m v^2)/r#

We can take logs and say that:

#ln F = ln ((m v^2)/r) #

#= ln m + ln v^2 - ln r#

#= ln m + 2 ln v - ln r#

Using differentials:

#(dF)/F = (dm)/m + 2 (dv)/v - (dr)/r#

# = 2% + 2 * 1.3% - 4% = 0.6%#

The formula for error propagation using standard deviations:

#(sigmaF)/|F|=sqrt(((sigmaa)/|a|)^2+((sigmab)/|b|)^2+((sigmac)/|c|)^2+...)#

Where a, b, c, ... are parameters used to determine the uncertainty of #F#.

#(sigmaF)/|F|# is basically a percentage in error if we multiply by 100%. Therefore,

Uncertainty in your centripetal force is #sqrt(2^2+1.3^2+4^2)=4.65725%#

Round it off to get #4.66%#.

There is a more robust way of measuring uncertainties using calculus and it is my go to formula.

Uncertainty of a quantity, #sigmaQ=sqrt((sigmaa(delQ)/(dela))^2+(sigmab(delQ)/(delb))^2+(sigmac(delQ)/(delc))^2+...)#

#(sigmaa(delQ)/(dela))# is basically #sigmaa# also known as the uncertainty to be multiplied by the derivative of #Q# with respect to parameter #a#.

Cheers.