Car movement physics

I want to model a car movement.

The equations are:

[tex]\sum[/tex]F = ma

[tex]\sum[/tex]T = m [tex]\alpha[/tex]

The forces are, weight of the car, normal force and f the friccional force, but also the engine provides a constant rotational acceleration in my model.

I understand that the frictional force is the one that moves the car, so:

f = ma

But also the movement of the engine generates Torque, and I can't realize how to connect this with the torque of the friccional force. Because if the car engine stop the frictional force stop the wheel but when the car engine is connected to the wheel they must oppose.

It's correct to say something like:
Torque (of car engine) - Tf (of frictional force) = I[tex]\alpha[/tex]

¿Does the frictional forces opposes to the rotation of the wheel car in the rotational movement??

I can't complete the movement description.

 

I can't edit the post, the formulas are "wrong" because I never use latex.

I want to solve the problem thinking of the tire as a solid ¿body? (I don't know how translate it) using these equations.

[tex]\sum F = ma[/tex]

[tex]\sum T = I \alpha[/tex]

I know the Torque of the car and I want to know how this is translated into equations, I've think something like:

[tex]\f (frictionalForce) = ma[/tex]

[tex]\sum T(engine) - T(frictionalForce) = I \alpha[/tex]

But I'm not sure if it's right to express the Torque of the car in that way.

 

Thank you for the welcome and thank you for answering, but I can't understand you completely what you are saying.

On ice the car doesn't move but the tire must spin if you're accelerating, so I don't know how to connect the engine torque that's it is providing to the wheel so that it can spin without moving on ice. That's why I added a Torque for engine. The frictional force in the Newton third law is the one that gives the acceleration but it also generates torque. At least that's what I'm thinking because that frictional force is applied over the surface and I'm taking moment over the center of the tire. The torque in the equation was negative because of the coordinate system that I doesn't draw.

On ice the rotational coefficient tends to 0, so that no force is applying. But in other cases there must be some rotational coefficient.

[tex]f = rollingFriction[/tex]

[tex]Tf = torqueOfRollingFriction[/tex]

[tex]Te = torqueOfEngine[/tex]


[tex]f = ma[/tex]

[tex]Tf - Te = I\alpha[/tex]

[tex]Tf = \mu_{r} N[/tex]

I know that there is friction from air and that's really important but that depends on the speed of the car, so if it's moving very slow the air friction could be avoided and the internal part of the car also have but I just want to understand this first part.