Sorry for the late reply - I've been offline for a while now. This was my first effort at panning at a Formula 1 race and therefore there was a lot of trial and error.
Fully agree with Thomas - check out the video workshop.
The difficulty I faced was that a Formula 1 car is always either accelerating of decelerating. If it is going at a constant speed then it is not set up correctly for the track. Therefore it was a bit more difficult than expected to pan smoothly and get sharp results, while keeping the shutter speed as slow as possible.
I started off at shutter speeds of around 1/100th and 1/200th but couldn't get the car sharp enough, but speeding up the shutter speed to around 1/500th seemed to do the trick with the car, while maintaining a bit of blur in the wheels. I haven't tried it yet, but I would imagine it's a similar case of trial and error that people go through at air shows with propeller aircraft and helicopters - trying to maintain the balance between sharp subject and pleasant blur on the prop/blades. With the slower cars in the support races it was easier to pan as the acceleration and deceleration aren't as dramatic, and therefore it was possible to slow the shutter speed down. Here's an example:
1 - 1/1600th second - no motion blur and the car could be at a standstill:
2 - 1/320th second - introducing a bit more blur into the wheels and background
Looking through the exif data, these were mainly taken with the humble 70-300mm VR lens, which did a great job. Unfortunately as the race itself started at dusk and ran into the night it wasn't fast enough to capture any decent results at that time. I would have needed an f2.8 70-200mm to maintain 1/500th in that light, and still have to pump up the ISO.