no this sure isn't normal...usually when there is a loss of fur or 'ripping' out its always due to allergies...the allergies can be inhaled, ingested or environmental.
I am assuming the food and litter has remained unchanged. that makes me think its either something in the house your kitty is reacting too....was there a product used to clean the carpets..for instance.
Or fleas? flea allergy can also cause this to happen. copy the link below for more info and photos..(some of it is related to dogs but cats have same symptoms..so read it all)
the only thing I DO NOT AGREE with is the use of steroids!!!! much better to find the cause and eliminate IT, not just treat the symptoms and cause other health problems...
http://www.marvistavet.com/html/body_inhalant_allergies.html
no its not really normal. she is in major stress mode. thats a lot of stress for a lil cat. try to keep her calm and she will calm down and stop doing this. i cant tell you when though.
how is she getting along with the new cat?