Question

What are possible reasons for the differences between the measured and calculated values of centripetal force?

Answer 1

They are both the same formula [except you left the mass m out of the second one]. The v = wr; where w = 2pi f and f is the frequency of rotation or revolution, w is the angular velocity, and v is the tangential/linear velocity.

Plug this into F = mv^2/r = m (wr)^2/r = m w^2 r = m (2pi f)^2 r = m 4 pi^2 f^2 r QED.

You use the form for F that has the variables you are given values for. For example, if you are given v, use the first form, but if you are given f use the last one.

Now, having said this, these are not the formulae for centripetal force. They are all for centrifugal force which is the reaction force to centripetal force. The real force, centripetal force, typically comes from some sort of attraction, like the force of gravity W = GmM/r^2 or EM force Eq = kq^2/r^2 between two dissimilar charges. Even tension on a cord as it is swung around with a mass on the end can be the centripetal, real force.