Reduction of diphthongs to short vowels (/waɪz/ -> /'wɪz.əd/)

Solution 1:

There are indeed five diphthongs/long vowels that reduce to a short vowels in some inflections of words. This is a consequence of the Great Vowel Shift: originally, in Middle English, the vowels /aɪ/ and /ɪ/ were simply the long and short versions of the same vowel: /iː/ and /i/ (so crime was pronounced something like we pronounce cream today). The Great Vowel Shift changed all the long vowels substantially, and left the short ones more or less the same.

The five pairs are:

diphthong /aɪ/ to short vowel /ɪ/ (crime, criminal),
diphthong /aʊ/ to short vowel /ʌ/ (foundation, fundamental),
diphthong /eɪ/ to short vowel /æ/ (nation, national),
diphthong /əʊ/ to short vowel /ɒ/ (code, codify),
long vowel /iː/ to short vowel /ɛ/ (brief, brevity).

John Well's Phonetic Blog mentions this in a discussion of why English spelling is so difficult:

Then came major sound changes, notably the Great Vowel Shift, which left us with sets of related words in which the common element is still spelt identically but nowadays pronounced very differently, and in which medieval scribes and printers opted to follow the sense rather than the sound: crime — criminal, type — typical, cave — cavity and so on.

Does this affect all inflected words? No, there are numerous exceptions, like proud, pride, where the vowels are different not because of the Great Vowel Shift, but because they were different in Old English; and scene, scenic, scenery, where the vowel doesn't change with inflections, even though it changes in similar words (zeal, zealot, zealotry). The vowel /iː/ may be conserved in scenic, scenery because the inflected forms date to after the Great Vowel Shift.

Solution 2:

As explained in Peter Shor's answer, Middle English had five sets of long and short vowels. Both the long and short vowels had almost the same vowel quality; the difference was only length i.e. the long vowels were simply long.

In certain environments, especially before two or more unstressed syllables, the long vowels became shortened. For example, as Peter Shor said, crime was pronounced /ˈkriːm(ə)/ and criminal /ˈkriːminəl/: the /iː/ in criminal became /i/ because it was followed by two more syllables. Later on, the Great Vowel Shift changed the vowel qualities of almost all the long vowels, so the /iː/ of crime became /aɪ/.

This process of shortening is called Trisyllabic Laxing and according to Trask's Historical Linguisitcs: ‘At one time, this rule applied to all relevant cases; it was therefore purely a phonological rule, a constraint upon what was pronounceable in English’. Later on, it ceased to be a part of English phonology, however, its remnants can still be found in Modern English:

• Sincere/sincerity /sɪnˈsɪə/ → sincerity /sɪnˈser.ə.ti/
• Pronounce/pronunciation /prəˈnaʊns/ → pronunciation /prəˌnʌn.siˈeɪ.ʃən/
• Derive/derivative /dɪˈraɪv/ → /dɪˈrɪv.ə.tɪv/
• Christ/Christmas /kraɪst/ → /ˈkrɪs.məs/
• Impede/impediment /ɪmˈpiːd/ → /ɪmˈped.ɪ.mənt/
• Holy/holiday /ˈhəʊli/ → /ˈhɒlɪdeɪ/

In some cases such as pronounce/pronunciation, announce/annunciation, profound/profundity, it also changed the spelling. The south/southern idiosyncrasy is also because of TSL: southern was a three-syllable word (/ˈsuːðərnə/) when TSL applied, the terminal 'ə' was later on lost and gave us /ˈsʌðən/.

Although there are so many exceptions such as words ending in -ness (mindfulness, loneliness etc) and later borrowings such as obese/obesity ^[Wikipedia]. In privacy, TSL applies in BrE, but not in AmE, nightingale,

_{Most of the transcriptions in this answer are from Cambridge Dictionary}