Talis Koton

 Bereishis (9:23) And Shem and Japheth took a garment, and laid it upon both their shoulders, and went backward, and covered the nakedness of their father; and their faces were backward, and they saw not their father’s nakedness

Rashi (Bereishis 9:23) And he took”, in order to teach regarding Shem that he devoted himself to this duty with more eagerness than Japheth. Therefore have Shem’s sons received the privilege of wearing the cloak that has fringes,

Igros Moshe (OC I #2) Question: Tzitzis of wool for a garment that is a different material than its wool corners? Answer It is clear that one needs to make the tzitzis of the same material as the garment. For example if the garment is silk and the corners are cotton. The derasha that tzitzis should be like the corners means like the garment. Thus for those who want to follow the stringency of the Maharam MeRoutenberg that wool tzitsis do not exempt other species it is not relevant that the corners are wool if the garment is silk and cotton.  Thus a silk garment needs silk tzitzis

Igros Moshe (OC I #2) Question:People who can’t wear a wool talis koton in the summer and they wear a talis koton of other material yet the tzitzis are still made of wool since the halacha is not like the view of the Maharam MeRoutenberg. Answer However it is definitely appropriate for a baal nefesh to be strict to only wear a wool talis Koton if at all possible in order to fulfill all views. 

Igros Moshe (OC II #1) Question: Do garments of synthetic material such as nylon and rayon that are worn in the hot summer require tzitzis? Answer  It seems reasonable to me that garments made from synthetic material should be exempt from tzisis.  This is obvious from the fact that a leather garment does not require tzitzis because only garments made from from threads like that of wool and linen need tzitzis. .Even if leather was made into strings and woven it would still be exempt from tzitzis since it is not typically a woven materia and thus such a garment is not considered a woven garment and is thus exempt from tzitzis. Consequently garments of these synthetic materials which don’t inherently require weaving from threads should be exempt from tzitzis. But perhaps there is a rabbinic decree that all garments need tzitzis which seems to be the view of the Rambam that tzitzis are reminders to do mitzvos. However the Rambam explicitly exempts leather garments from tzitzis and thus would likely also exempt these synthetic materials.  So it could be that there is a decree for all garments that are woven like wool and linen.  However to wear these garments in hot weather – even cotton is exempt -  from the Torah obligation of tzitzis according to the Rambam and Shulchan Aruch and thus do not fulfill the Torah obligation. This is a problem during a time of G-d’s anger that one is not protected from harm.  However according to the Rema and the majority of  poskim that all garments require tzitzis according to the Torah  and thus they can clearly be relied upon even not to be strict to wear only a woolen garment even if only because of the heat. Nevertheless a baal nefesh should be strict to only wear a woolen talis Koton. 

Igros Moshe (OC IV #4) Question Is there an obligation to wear a garment that requires tzitzis? Answer  Clearly there is no obligation except to have tzitzis if you are wearing a garment that requires tzitzis. However since it has become customary for Jews to wear a garment that requires tzitzis it is forbidden to ignore this custom which is learned from the verse in Mishlei “Do not desert the teachings of your mother.” .  In fact since this custom results in doing a mitzva it is surely obligatory. There are many important reasons given for weaing tzitzis (Menachos 43b). We learn also that it protects at the time of G-d’s anger  and thus even if he doesn’t own a proper garment he should buy one for protection. 

Igros Moshe (OC V #20.25) Question Is there an obligation to wear a four corned garment and to say a beracha on tzitzis? Answer You say it is apparently a widespread practice in yeshivos that the young men do not say a beracha on tzitzis in the morning when they put on a talis Koton. This obviously against the halacha if the garment is at least three quarters of an amah on each side except for the neck hole. If it is too small than that explains the absence of a beracha. But I don’t understand why a ben Torah would wear a talis Koton that doesn’t require tzitzis. Even if there were no obligation to wear tzitzis but it protects at a time of G-d’s anger. Therefore it it is obvious that the heads of the yeshiva need to warn all the students over the age of 13 to wear a garment that requires tzitzis.  Because of this I even wear a wool talis koton even in the hot summer to fulfill the Torah requirement. While  for yeshiva students it is not necessary to be so strict because of the difficulty of the heat, nevertheless they need to wear a proper sized talis koton of other materials such as cotton but not from synthetic material such as nylon and rayon which are exempt from tzitzis. 

 Igros Moshe (YD II #137) Question Someone who takes off a talis Koton at night does he need to put it back on at night? Answer  From the Magen Avraham it would seem prohibited. However perhaps only a regular talis is prohibited because it requires a beracha. However it seems obvious that not redressing will not result in punishment even at a time of G-d’s anger. Therefore I don’t see that it is prohibited to not put it back on and it is not even a stringency especially according to the Bach.