[Tristan Lall]

If you use polycarbonate or acrylic, you'll be annoyed when it gets scratched by just about anything that you put on top. Plus, some household chemicals will cloud or discolour plastic. The only thing that's really practical (with similar aesthetic properties) is a thick piece of glass, probably on the order of 1/2" to 5/8" thick—you need to be able to put significant weight on it, just for safety (you don't want it collapsing when someone leans on it, or worse, mistakes it for a seat, and you want it to be heavy and rigid enough to stay level and planar, even if the stuff on top is unbalanced). See if you can find someone who will sell you a 4' circle of tempered glass, with a finished edge (rough, polished, beveled—anything without sharp edges).

If you must use thin plastic, because of cost, don't extend out to 4'; instead, keep the overhangs small (2" or so, maybe), so that you don't inadvertently tip the table by leaning on the top.

Alternatively, if you don't mind damaging the tire, drill holes through it, and fasten the top with through-bolts—maybe using some 1/2" flat socket-head cap screws, recessed into the tabletop and secured on the inside of the tire with nuts. That will at least retain the look—but if I had a souvenir like that, I wouldn't necessarily want to drill through it.

And, by the way, recent F1 tires are made by Bridgestone, or previously, Michelin. It's been a while since Goodyear made tires for F1 cars themselves—maybe it's another racing series that you're thinking of? In fact, Goodyear makes tires called F1, but they aren't F1 tires!