If you want to roll your own, you still may want to look at some (free source) physics engines (no pun intended) that are out there. Specifically for rigging vehicles, I'm only familiar with ODE. I'm sure there are other examples for Bullet, etc.
What physics is involved in a car game?
If you're not already familiar with the basic application of forces (f=ma, force-at-position=torque+force-at-CG, springs/dampers, etc), you'll want to brush up on them. Burnt_Fyr provides a pretty good list of the parts of the system you may want to model. You may also want to google for information on "how a car works."
You can start with a basic model, e.g.:
1. rear-end-drive means wheels fixed with position to the CG. Forces where the tire meets the road - gravity, rolling friction, side forces, etc.
2. front-end-steering means the user controls the angle the wheels make with the CG. Friction perpendicular to the rolling direction causes the car to rotate (i.e., turn).
Go from there:
a. Rear-end-drive - frictional force from wheel rotation, through the suspension to the CG provides one of the forces on the CG. Also, work your way from the wheels, through the drive axle, the diff, the engine, etc., as Burnt_Fyr describes (in reverse) to get the source of that wheel rotation.
b. Front-end - work your way from the tire against the ground, back up the suspension to the center of CG.
In general, you'll start with all the forces that act on each of the four wheels. For each of those, calculate the force and torque on the CG for it. Sum all the forces and apply F=Ma. Sum all the torques and calculate the angular velocity of the CG.
Edited by Buckeye, 20 May 2014 - 04:43 PM.