Low-rate dynamic contact angles and static advancing contact angles of 13 liquids were measured, respectively, by axisymmetric drop shape analysis (ADSA) and a conventional goniometer technique, on two copolymers, poly(propene-alt-N-(n-propyl)maleimide) and poly(propene-alt-N-(n-hexyl)maleimide); both have polar groups. In the case of the former technique for measuring contact angles (at very low velocity of the three-phase contact line), very complex contact angle responses were observed for some solid-liquid systems. In a specific case, slip and stick contact angle behavior occurs where the contact angle increases steadily by as much as 35 degrees at constant three-phase contact radius and subsequently decreases sharply due to a sudden jump in the three-phase contact line. Thus, circumspection is necessary in the decision whether or not the experimental contact angles can be used to interpret surface energetics in conjunction with Young’s equation and whether the solid-liquid systems violate the basic assumptions made in all surface energetics approaches. It was shown that if one omits the inconclusive contact angle measurements, the values of gamma(lv) cos theta change smoothly with gamma(lv) for these copolymers in a pattern already well-known for nonpolar surfaces. Goniometer and ADSA contact angle measurements were shown to be essentially identical for solid-liquid systems which have constant contact angles. In the specific case of the slip/stick mechanism using a goniometer for the contact angle measurements, the observed static advancing angle corresponds to the maximum angle of the entire slip/stick behavior, as registered by the automated axisymmetric drop shape analysis. Thus, conventional goniometer measurements may produce a mixture of meaningful and meaningless contact angles, with no criteria to distinguish between the two.