You mean 1gb memory, right? Anyways, it shouldn't have a problem playing youtube videos. Are you sure it's not your internet being slow? Also YouTube tends to slow down nowadays for no apparent reason. Another explanation that is very unlikely is that maybe your DRAM (regular ram as you probably know it) is malfunctioning.
Carlos, have a total graphics memory of 2791MB wich are divided as follows: 1024MB dedicated graphics mem, and 1767MB of shared graphics mem. Though system performance test with Win 7 shows that the dedicated mem is performing at 5.2??? which is a value given in a scale of 1.0 to 7.9. I do not know what that means however.