Let’s say one is listening to an online shiur. He has to do an assignment for school, so he turns the shiur off. Would sources deem this as Bitul Torah? Please cite sources.
Rav Moshe Feinstein (Igros Moshe, Choshen Mishpat II:30) was asked whether a student may cheat on the Regents, as it’s required for him to take it, but studying for it would detract from learning Torah. After saying that it’s forbidden not only because of Dina d’Malchusa but also by Torah law, he turns to address the premise of the question: that studying is Bitul Torah.
ואם חשקה נפשו בתורה אין לו לדאוג שמא לא ידע כל כך ולא יהיה לו סימן טוב עלייהו אבל האמת שאין בזה ענין בטול תורה שמאחר שהולך ללמוד למודי חול הוא רק עצלות בעלמא כשלומד באופן שלא לידע כי הזמן הוא עכ״פ מבטל ואדרבה מתרגל שלא לידע מה שלומד ומתרגל לעצילות
If his soul desires Torah, he should not be worried maybe he doesn’t know so much and there will not be a good Siman on him. In truth, there is not Bitul Torah in this, for once he’s going to learn secular subjects, it’s merely ordinary laziness if he learns in a way that he doesn’t know it, as the time will in any event be wasted. To the contrary, he regularly acts to not know what he learns, and he regularly acts toward laziness.
Therefore, if one is in school and is learning secular subjects, it is not Bitul Torah to do his homework or whatever else is necessary to retain that information, as the other option is letting the time in class go to waste.