There are a few rules regarding the letter Raa.
1. Raa with a regular Harakah (Dhamma, fatha, kasra/Zabar, zer, pesh).
If the raa has a fatha/zabar, or Dhamma/pesh, it will be pronounced with a full mouth.
Examples:
الرَّحْمـَنِ الرَّحِيمِ
يَشْعُرُونَ
If the raa has a kasrah/zer under it, it will be pronounced with an empty mouth.
Examples:
غَيرِ المَغضُوبِ
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2. Raa saakin (with a jazm/sukoon on it, or because of stopping).
If the raa is saakin, we look at the letter before it. If that letter has fatha/zabar on it, the raa will be pronounced with a full mouth.
Examples:
أَنذَرْتَهُمْ
If the letter before the raa saakin has a kasrah, it will be pronounced with an empty mouth. (There are a few exceptions to this rule, but they are rare).
Examples:
تُنذِرْهُمْ
التَّكَاثُرُ (when stopping on the raa)
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3. Raa is saakin because of stopping at an ayah, and the letter before it is saakin. In this case you must look at the second letter before the raa. If it has dhamma/pesh or fatha/zabar, it will be pronounced with a full mouth.
Examples:
وَالْعَصْرِ
خُسْرٍ
In the above example, the letters Ain and Khaa have fatha/zabar and Dhamma/pesh respectively, so the raa will be pronounced with a full mouth.
If the second letter has kasrah, the raa will be pronounced with an empty mouth.
Example:
ذِي الذِّكْرِ (when stopping on the raa)
In the above example, the letter Zaal has kasrah, so raa will be pronounced empty mouth.
Listen to soundbyte for more details.