In regard to Max Torque’s post, yes, kids learn very early that “NO” is a word of great power…why do you think it is so popular with toddlers? 
I had very strong-willed kids myself (go figure:p), and time-out was never a case of simply ordering them to a corner…it involved physical removal and enforcement (removing them and then putting them back over and over).
I’m actually not a huge fan of time-out as usually practiced. I agree with the idea of a time to calm down and regain control, but not as punishment, and it is often very difficult to separate the two in practice. Time Out as usually defined has always been a last resort for me, as both a teacher and a parent.
I prefer the approach of removing the child from the situation and diverting them to another activity until they calm down and discussing (as far as is possible, depending on age) the initiating issue. No real need to make it an official thing (“a time out”)…just say, “You seem really upset/frustrated/tired. Come sit with me or sit over here and do this puzzle or look at this book for a while until you feel better/calm down. When you do, you can go back and play. I can’t let you hurt someone.” (and enforce it…don’t allow them to rejoin “society” until they are actually calmed down)
It can also be helpful to model use of a “time out” yourself…when you feel yourself getting frustrated or irriatated, say, “Whew! I’m going to go sit over here for a few minutes and calm down! I need a time out.” You set an example of a safe, rational way to deal with those feelings. I’ve seen 2 and 3 yr olds who would put THEMSELVES in “time out” when they were getting frustrated as a result of such modeling by adults.
Even better is catching the melt-down BEFORE it starts and diverting…I spent a lot of years doing this in classrooms full of 2-4 yr olds, and it is usually possible to spot a child getting ready to bite or pull hair or otherwise lose it over a dispute, swoop in, distract and avert, thereby eliminating the need for “official time out”. You have to be observant for the signs and it’s not always possible, but IME at least 80% of such incidents can be prevented.
2 year olds are typically not capable of controlling themselves to any great degree in the face of hunger, tiredness, frustration and usually don’t get much out of time-out when it is termed that way and used as an after the fact penalty. They do benefit from an attentive parent or caregiver who acts, calmly and matter of factly, to PREVENT them from performing their inappropriate actions and remedy the underlying causes.
Just my 2 cents…good luck! 