I am trying to do some car calculations for a game.
I have a tyre (radius $r$, inertia $I$) rotating around it's axle with an angular velocity $\omega$ faster than the center of mass is moving across the surface. So the tyre is not rolling along the ground, but slipping. The surface has a friction coefficient $\mu$. The tyre is pressed down by the car with a weight $N$
I need to calculate two things.
- The force the tyre exerts on the ground.
- The resulting (de)acceleration of the tyre.
Imagine a car doing a wheelspin. I need to find the force the excess speed of the tyre transfers to the ground, giving an acceleration to the car, and thereby also de deacceleration of the tyre.
I have calculations for the external forces (engine, brakes, drag, lateral slipping) and this is the final piece to complete the puzzle. So help is much appreciated, as i have been trying to solve this in a myriad of ways, with no success.
//Edited - It is the wheels connected to the enigne i am trying to calculate. However i am in this case not interested in the torque coming from the engine, only actions from the extra energy stored in wheel from building up the spin.
The engine provides a torque $\tau$ on the tyre