Just one of those words with several different regional pronunciations.
If you can believe Wikipedia - https://en.wikipedia.org/wiki/American_and_British_English_s... - Mom is sporadically regionally found in the UK (e.g., in West Midlands English). Some British and Irish dialects have mam,[117] and this is often used in Northern English, Hiberno-English, and Welsh English. Scottish English may also use mam, ma, or maw. In the American region of New England, especially in the case of the Boston accent, the British pronunciation of mum is often retained, while it is still spelled mom. In Canada, there are both mom and mum; Canadians often say mum and write mom.[118] In Australia and New Zealand, mum is used. In the sense of a preserved corpse, mummy is always used.
Just one of many pronunciation drifts that occurred between the UK and its American colonies at some point between 1620 and 1788. Largely it seems the Americans kept the old pronunciations while the mother country changed theirs, which is why the English of Shakespeare's time sounds a bit American.
It's not quite like that. American pronunciation change as well. Here's an example of how linguist reconstruct the original pronunciation of Shakespeare plays: http://youtu.be/gPlpphT7n9s
It really has more elements that sound like West Country accent, Irish English, or even Scots/Ulster Scots.
Now what's interesting is that this sound is closer to how an American might pronounce a short "o" (I think of a southern belle fanning herself and saying "lawd it's haaaht") and how an Englishman might say a short "u". It's not exactly the same vowel but I can see how it develops.
Both versions of English think babies say "mama", but you can't shorten that to "mam" because you'd use a different "a" to pronounce that.
If you can believe Wikipedia - https://en.wikipedia.org/wiki/American_and_British_English_s... - Mom is sporadically regionally found in the UK (e.g., in West Midlands English). Some British and Irish dialects have mam,[117] and this is often used in Northern English, Hiberno-English, and Welsh English. Scottish English may also use mam, ma, or maw. In the American region of New England, especially in the case of the Boston accent, the British pronunciation of mum is often retained, while it is still spelled mom. In Canada, there are both mom and mum; Canadians often say mum and write mom.[118] In Australia and New Zealand, mum is used. In the sense of a preserved corpse, mummy is always used.