# Does a car move if the wheels were slipping?

If you put the transmission in the 1st gear, floor the gas pedal, and then suddenly release the clutch, the wheels will slip due to the lack of static friction to move the car relative to the force applied to the wheels, right? Now, my question is: will the wheels keep slipping and the car remain stationary if the gas pedal keeps floored, or will it move after a period of time? And if it moves, why will the wheels stop slipping and start to roll though the force applied from the engine stays the same, and of course, the static friction is constant?

• What sideways force exists between the wheels and the ground when the tires are slipping? Is it zero? – BowlOfRed Apr 28 '17 at 18:21
• @BowlOfRed IDK? Is there any other forces other than rolling resistance, static friction and kinetic friction in case of slippage? – user3407319 Apr 28 '17 at 18:47
• It can't be static since it's slipping. Rolling resistance wouldn't be modeled at this level. So probably kinetic friction would be an excellent place to start. – BowlOfRed Apr 28 '17 at 18:51

If you put the transmission in the 1st gear, floor the gas pedal, and then suddenly release the clutch, the wheels will slip due to the lack of static friction to move the car relative to the force applied to the wheels, right?

Wrong, the wheels slip because the torque applied to the wheels by the drive train is greater than the torque applied by the kinetic friction between the ground and the slipping tire.

Now, my question is: will the wheels keep slipping and the car remain stationary if the gas pedal keeps floored, or will it move after a period of time?

If by slipping, you mean slipping perfectly, i.e. that the car is not moving forward at all, then the car will remain stationary until something upsets that perfection. In order to be slipping perfectly, the frictional force has to be zero, that means that you need to get the wheel turning fast enough such that $\mu_k(v) = 0$. Otherwise, if the kinetic frictional force ($F = \mu_k N$) is greater than zero, then the car must be moving forward already and you aren't slipping perfectly and the system is much more complicated, but the car is already moving forward, so your question doesn't really apply.

And if it moves, why will the wheels stop slipping and start to roll though the force applied from the engine stays the same, and of course, the static friction is constant?

The friction is not static, it is by definition kinetic because the wheel is slipping. If the friction force is constant (not static), then the car will accelerate forward until the torque from the ground friction forces compensates for the torque provided by the drive train, and then the car will move forward at constant velocity.

• Isn't it static friction what makes car wheels roll forward? – user3407319 Apr 28 '17 at 18:54
• Only if they aren't slipping. If they are slipping, then the wheels are experiencing kinetic friction. This is why anti-lock brakes work but are counter intuitive. For most road conditions the coefficient of static friction is larger than the coefficient of kinetic friction. Conversely, this is why your car gets up to speed faster if the wheels don't slip. – Finncent Price Apr 28 '17 at 19:14
• Then what did I say wring in the first question? I said it slips because static friction is not enough, right? – user3407319 Apr 28 '17 at 19:17
• Static friction and kinetic friction are different because static friction occurs when the two bodies are at rest at the point(s) of contact. Kinetic friction occurs when the two bodies are moving at the point(s) of contact. If the wheel is slipping, there is no static friction between the wheel and the ground. It is not that it is insufficient, it is that it is non-existent by definition. Further, kinetic friction can cause the car to move forward, it just won't do as good a job as static friction. – Finncent Price Apr 28 '17 at 19:20
• So the slippage has nothing to do with static friction being little, but it doesn't even exist? So what else determines if static or kinetic friction is in control? Also, is there an equation to determine the amount of motion in the car in case of kinetic friction when the wheel is slipping, I suppose it is a lot less? – user3407319 Apr 28 '17 at 19:25