Do I need a physics engine

Whether you 'need' a physics engine depends on the quality/style of game you're trying to make.

That said, for a racing game, physics is usually fairly important. If you want rolling, etc... I would definitely recommend it.

I've heard bullet physics is pretty good, although I haven't used it myself. They have a java port (jbullet).

Ill build my own engine I was just curious if there was another way for me to do it.

yes, do the physics simulation yourself. But there are libraries available so why reinvent the wheel? I would also think twice before building an engine yourself, did you see the JMonkey Engine?

I would advise to use a physics engine. A Physics and collision detection engine is not something you can pick up and write in a month. Especially for car racing.

If this is just a personal project I don't see the problem in writing your own physics engine if it is something you are really, really interested in; although it may well be better to do so as a seperate project to avoid complications.

Why re-invent the wheel? To fully understand how it works and learn from it!