Looking at the structure of an amino acid (as a zwitterion), it seems that the part of the molecule with the amino group and the carboxylic acid group are quite polar (the amino group has a positive hydrogen and the carboxylic acid group has a negative oxygen). However, my textbook says that the character of the R group completely determines the polarity of the molecule (i.e. if R is non-polar, the molecule is non-polar). Why is this?
There are two things at play here and you need to mentally separate them.
When seen as molecules, all amino acids are polar to at least some degree. Most of them are very polar, especially when compared to other organic molecules. This is (obviously) due to the carboxylic acid and amino groups both of which are very polar functional groups and both of which are ionised in neutral aquaeous solution.
However, it is desirable to categorise the different amino acids into various groups, to better explain their individual contributions to an overall peptide or protein structure. As all amino acids have a carboxylic and amino group and as these groups are connected in peptide bonds to form the peptide or protein backbone, these two groups alone are not able to distinguish between the different amino acids.
For this reason, the amino acids have been classified according to their residue R. If the residue contains only carbon and hydrogen atoms (e.g. Gly, Ala, Val, Leu, Ile), it is a non-polar residue and thus these amino acids are classified as ‘non-polar amino acids’ in simplistic terms. In a peptide or protein, these amino acids’ non-polar side chains will usually act as non-polar domains within the tertiary structure
A similar case can be made for the ‘charged’ amino acids (Glu, Asp, Lys, Arg): obviously and trivially, all amino acids have charged groups when dissolved in water but only those four have a charged side chain. So only these four are able to build up salt bridges to cross-stabilise tertiary structures and are thus classed as charged.
All amino acids have the capability to form the zwitter ion...but that doesnt necessarily make all of them polar....consider the example of a saponification reaction...we have a polar end and a non polar alkyl group attacked to it making that whole part of the chain hydrophobic...and non polar Indeed since the general structure of an amino acid being NH2-CH(R)-COOH The R group has a significant part to play in determining if an amino acid is polar or not...which makes amino acids like alanine, cysteine, glycine, isoleucine, leucine, methionine, phenylalanine, proline, tryptophan, tyrosine and valine show more of a non polar character than polar