is this supposed to be loose?

My bike, 1983 KZ550 m1, has been running like a champ ever since I saved her from a junk yard. But a few weeks back, I took her for a little highway ride for an hour. I stopped to top off the gas for the return ride. My bike decided that she wasn't going to run anymore. Instead, she sounded like the battery was low, then squealed a few times. I tried jumping it off a non running car. Same result. I picked her up and brought her back home. I've been busy since then. Today I was able to take out the starter. I jumped the starter to see how it was. It spun strong and freely. I set the battery on a charger as well. So far the green light to say it's fully charged hasn't come on. I checked the sprocket that the starter connects to. (What is it called, by the way?) I did attach a picture of it. Well it seems to have some play in it. It doesn't seem normal... Well it probably isn't normal. Oh, and I also opened my starter to clean it. It had a good amount of soot in it. And I found two of the brushes were failing. So now...

A) the sprocket (which I don't know the name of) shouldn't have lateral play in it? And if not, how does one go about to work on it? Hard job? I'm pretty mechanically inclined.

recommendations on where to buy starter brushes. When I bought the bike in January, I bought a rebuild kit on Amazon. It came with new bearings, brushes, o rings.. only was $12 or so. Just buy from them again?

C) just waiting on a repair manual, but this place is like a digital manual in itself.

Thanks guys.

Try these places:
A. www.psep.biz/store/mitsuba_starter_motors_page_2.htm

B. www.nationsautoelectric.com/Kawasaki.html

C. www.whitedogbikes.com/cat--Kawasaki-Star...-Starter-Motors.html

D. www.ricksmotorsportelectrics.com/starters.php

E. www.dbelectrical.com/

F. http://.www.nationsautoelectric.com/Kawasaki.html

G. http:// www.dbelectrical.com/

Thank you for the links. As far as the brushes go, I think I decided to buy from Amazon. The rebuild kit is pretty good fo $18 flat. Two day shipping is great too.

Now as far as that sprocket goes, is that little movement remotely normal?

My battery is toast too. One day I'll splurge on a "real" battery. Ha. All I can afford right now is a (N)ever start from Wal Mart.

It has been 16 days since I've ridden my bike. As my mentor would say..."That's no bueno por sh*t." Excuse that Marine's language.