bugün çok meşgulüm is correct, I would use it already

Meşgul is from Arabic. Words with arabic roots sometimes change, in the dictionary you will see this as: meşgul / -lü

When you add a suffix after such words, it takes the soft one.

Compare:

meşgul - meşgulüm, not meşgulum (I am busy)

kalp - kalbim, not kalbım (my heart)

kabahat - kabahatim, not kabahatım (my mistake)

kanaat - kanaatindeyim, not kanaatındayım (I am of opinion)

is there a way to tell Arab borrowed words from Turkish, or is it just with practice. I would think you could tell by the vowels? being a-i or mixed like a-ı maybe?

Thank you for help 

Thanks for this

Are there other words that dont respect the vowel harmony ?

 I don´t know.. it doesn´t count for all words, kitap is arabic (which is clear from the fact that the two types of vowels, i and a, are in the same word.. you would not see that in a word of turkish origine), but still goes according to vowel harmony (kitabım).

You could understand the difference, but you would need to have knowledge of Arabic alphabet then you can realise what the original letters are (was it kef or kaf, sad or dad for example) and know if it should be a hard or a soft vowel. I dont know if theres a fast way to learn this. I suggest you look it up in the dictionary of this website and see if it shows ´lü´ (or smt else) and then just memorize and practice.

 There probably are many more But you learn them by time and by checking the dictionary.

Another example of ´irregularity´ when it comes to words of arab decent:

akıl /-lı

When you see this in the dictionary, a suffix is addid to the original root of the noun, which is ´akl´. So --> aklım, not akılım.

izin --> izninizle, not izininizle

"Hal" (situation)word is Arabic too, it doesn´t respect vowel harmony

Not Halım or Haldan, Halim and Halden is correct.

Meşgul word is Arabic, as Deli_kizin has explained. "u" is soft there. It is close to "ü" voice.

Once we were showing these voices with a "hat" over the character;

Meşgûl, hâl ... etc. But now we don´t use that.

By the way;

You can use "yoğun" word instead of "meşgul."

Yoğunum, yoğunsun, yoğun, yoğunuz, yoğunsunuz, yoğunlar. It shows respect to Turkish vowel and besides it is a Turkish word.

thx

turkishcobra //

As i see in dictionary it points "meşgul" for busy instead of "yoğun"

Because sometimes, it sounds as "meşgul" tells about the immediate business, "yoğun" is more general. I told "yoğun" because it doesn´t contradict with the vowel harmony and easier to pronounce.

According to the Turkish pronunciation rules, "g" at "meşgul" must have been turned into "k". At daily speech, we generally pronounce it as "meşkul", because "ş" is hard consonant.

And a small note: dictionaries do not have to meet all meanings of a word. Although "meşgul" is not a Turkish-rooted word, it is used more common, that´s why dictionary tells "meşgul".

thx

turkishcobra //