The crack wont cause it to shake, but if the tread is scalloped, that could cause it to shake. Regardless you should replace the tire, inspect the rear one also. Good chance the tires are old, given the year of the bike, and that it has been sitting. Would give you an opportunity to inspect the wheel bearings also.
2006 Ninja500R Purchased new July 2006, 0 miles. Miles as of January 2017 88652. It is a GO bike, not a SHOW bike.
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