2001 Hyundai Tiburon makes grinding noise while in motion

On first blush, sounds like you may have a bad CV joint or wheel bearing.

jack car up in back and rotate wheel by hand to see if one of the two have a grinding noise or doe s not rotate freely.. that would be the one with bad bearing.

The wheel bearing is press in. Remove the knuckle and use a hydraulic press to remove and install a new one.

Perhaps the cv joint.

Hello mpolci...The 2003 Tiburon was sold to the public with a defective clutch, it failed due to warpage and bad pressure plate... among other things. There are MANY class action lawsuits. Did you resurface or replace the flywheel when the clutch was replaced? Did you go with an aftermarket clutch kit, or factory? Also the slave cylinder on the 03 was known to have a defective valve.
You can try checking the levels and bleeding the system and if you still have problems, then it could be a release bearing, a loose clutch pad, or a broken pressure plate spring....If the clutch is still under warranty, i would return it to the installer.
Good luck, i hope this helps...please rate me a fixya.

Wheel HUB bearing... find out which one (possibly both).

That's a hub bearing. Replace the one that's doing it. I'm assuming this 'roar' is coming from the front, NOT the rear.

There are several sources from which to get your owner's and service manuals, including going to the manufacturer of the car, and these:

http://yourhandymanzone.com/Your_Handyman_Zone_How_To_Pages_Vehicle_Car_Zone_Cars_Trucks_Vans_Owners_Manual_Lost_Need_Replacement.htm

Yes autozone.com has a repair guide for your car,you will be able to get the steering knuckle off,this is where the bearing is but ir requires a press or an equivlant to remove and replace the bearing.

u will need to remove the brake cailper and the the brake rotor, then the hub retaining nut, that is a large metric nut, the bearing and hub must come off, then u will need to take this hub to a machine shop or the dealer and have the new bearing pressed in.
BCA/NATIONAL Part # 510078 {Ball Bearing Bore=1.5354" Outer Diameter=2.9134" Width=1.4173"}
Front Wheel PRICE: $47.99, PART SOURCE: Rockauto.com