Longitudal and lateral forces acting on tire (some questions)

Hi,

i've just started to work on my car 2d simulation project and i've
encountered some problems relative to some aspects on longitudal and
lateral forces. I was searching for any information and i didn't find
anything.

The questions:

1. If wheels blocked (front or rear or both) => the tire acts as rubber
friction material in opposite direction of car CM velocity, but if the
car spinning aroung it's CM => tires won't resists that rotation hence
blocked tire should resists in opp. dir of vector = sum of car CM
velocity + linear speed of angular velocity of tire connection point (V
= w*R, where w = angular velocity and R = radius = sqrt( wb^2/4 + wb*wd
+ wd^2/4 ), where wb = car wheelbase, wd = car width, so R = just
vector from CM of car to tire connection point).

2. If wheels are spinning then on each tire acts lateral and longitudal
forces if exists, let's say we have fwd car, so on front wheels we have
longitudal forces: engine power on tires and some roll frequency more
less than engine power, lateral forces: as i've read they are
perpendicular to the direction of tires, but what direction? i think,
direction of lateral forces on each wheel is defined by slip_ratio sign
(as i calculated later), right?

3. One more time about spinning of car, so Wcm != 0 and Vcm = 0, only
lateral forces cause car to stop rotating or something else?

Here is my approx. of slip ratio: for each wheel i've calculated it's
velocity vector (sum of CM linear velocity + linear velocity of tire
mount point, if the car's CM has angular velocity, hence
Vtotal_wheel_velocity = Vcm + Vtire_linear_velocity).
Then i've got cross product of wheel direction vector and total wheel
velocity vector. Then i've got z component of this vector as slip
ratio.
As i model 2d physics then Vtotal_wheel_velocity and Vcar_direction
lies on plane => cross product of those two vector will be vector
perpendicular to plane => only z component of result vector used.

Thanks in advance!!
Max