I have a 2004 Gsxr 1000 and the starter spins but the flywheel doesn't engage why is that

Hit starter and it does not engage engine but still the starter spins.

If you have tested the starter, and it is installed correctly, and it spins, my guess would be missing teeth on the flywheel.
A Ford starter needs 11 volts to engage so you could check to make sure you have that at the starter cable post.
You could also turn the crank a few degrees to see if the flywheel is warped or damaged.

check your flywheel & starter, one or both will be missing teeth, or the starter isn't "throwing out" yo engage flywheel

check key switch first, and fuse.

starter, take out and try across battery and it should whirr and jump out as if connecting with flywheel, if no spray the whole starter with WD40 inside and leave overnight. worked for me.

If the starter is spinning when you try to start but doesn't spin the engine over then you most likely have teeth missing off the flywheel ring gear. The facts that you say you have to push it and then it starts means the flywheel position changes and the starter has good teeth on the flywheel to engage. To confirm this next time the engine won't crank over remove the starter and look inside at the flywheel for missing flywheel teeth.

If the starter motor spins at high speed, but doesn't turn the engine until you whack it, the starter gear is not engaging the flywheel. Probably the engagement fork or the starter gear is worn out or sticky, or the solenoid isn't pushing it far enough.

If the starter motor is running, the solenoid is working. Is the "over running" spring, cup, and pin in place? Is the shifter fork for the starter shaft positioned correctly in the collar behind the Bendix.

Disconnect the battery, remove the primary cover, and take the solenoid off but leave the plunger for the solenoid in position. Now, with the solenoid off, pull the plunger back in the direction that the solenoid would pull it. Watch the starter shaft and make sure that it moves forward and engages flywheel. Take the starter off and make sure the small gear on the end of it is in good shape as well. Try that Bendix with your hand, It should turn one way but not the other. Even if it does, that doesn't mean it's good. If it turns in both directions, it is bad.

http://www.bikebandit.com/1972-harley-davidson-xlh/o/m1748#sch195980

Good Luck
Steve

If the starter wont turn...Id check / replace starter solonoid.
If the starter turns but doesn't engage the flywheel...I'd check / replace the bendix.
If starter checks good and bendix is good...I'd look at the teeth on the flywheel.

Hope this helps...

The starter sprocket wheel is thrusted into engaging the flywheel by a big solenoid. That solenoid is integral part of the starter motor. If the starter turn itself but it doesn't turns the engine then either it was incorrectly installed or the thrust solenoid is defective.
Simple test: take out the starter, attach it to a bench, connect to it thew power cables from a battery (the minus one to the body, the plus one to the big connector bolt) then short the big connector bolt to the small one with a screwdriver - the solenoid should activate, the sprocket should be thrusted forward and the motor should start spinning it.
If that doesn't happen then the starter you just bought is defective, replace it. If that happens the starter was incorrectly installed on the engine. Reinstall it correctly.