# How does friction accelerate a car after rest?

If a car moves using the friction force from the rotation of the wheels, shouldn't a car be unable to accelerate immediately after the car is at motion, since there will be a friction force of equal magnitude which opposes the movement of the car. I've been trying to think about how cars move for a while now (from a purely mathematical perspective), however I haven't been able to find any rotational velocity dependant equations for friction. The only idea that I have, which doesn't make that much sense is that the rotational friction is proportional to the centripetal force, however it doesn't seem to make that much sense...

Edit: I don't want to know about the specific parts of a car, how the wheels attain rotational velocity from the car or anything of that kind.

I think what you're imagining is what would happen if the car were a block of metal dragging on the road; the kinetic friction of a block of metal sliding on a road would make a force countering the forward drive. But the beauty of wheels is that they don't (or shouldn't) slide or drag at all. Instead the part of the wheel or tire that touches the road is always non-moving with respect to the road (i.e. unless it's skidding or sliding). So think of the drive wheels applying force to the road, and the road pushing back at the point where the wheels touch it, so that force propels the car forward in that instant. In the next instant, a different part of the tire touches the road and "repeats" that interaction but there's no kinetic friction, only static friction, because the bottom point of the tire is still non-moving with respect to the road. If that doesn't make sense, picture the bottom of the tire moving backward with respect to the car as the road also "moves backward" with respect to the car, and see how they move backward together.

• I see, so the friction direction depends entirely if the wheels are moving at a faster or slower rate than the car itself, accelerate the wheels and the friction force has the same direction as the movement therefore accelerating the car, if the wheels deaccelerate to lower than the cars speed and the friction force will have the opposite direction, but always with the same magnitude? Edit: By the way, is the friction force which accelerates the car the same that deaccelerates the wheels' rotation? Jul 25, 2021 at 0:24
• Exactly. The only way those forces aren't equal is if some energy is lost if the wheels slip against the road. As long as there's no skidding, the wheels just make a force-carrying connection between car and road. I like to imagine a cog-wheel vehicle en.wikipedia.org/wiki/Rack_railway to avoid confusion about friction. Static friction is actually the same concept anyway, but with microscopic "teeth". Kinetic friction is different, where the teeth break or jump over each other instead of staying in lock-step. Jul 25, 2021 at 0:30

If a car moves using the friction force from the rotation of the wheels, shouldn't a car be unable to accelerate immediately after the car is at motion, since there will be a friction force of equal magnitude which opposes the movement of the car.

The car drive shaft exerts a torque on the drive wheel which pushes back on the road. Then per Newton's 3rd law the static friction between the road and wheel exerts an equal and opposite force forward on the vehicle. Since that static friction force is the only external force acting on the vehicle in the forward direction it is the force that is responsible for accelerating the car. See the figure below.

The forces opposing the forward acceleration of the car are air resistance and various sources of mechanical kinetic friction (e.g., axle friction, and various sources of friction in the drive train components). There are no other forces opposing the acceleration except what is called rolling resistance. It is sometimes called rolling friction and is due to the inelastic squeezing and un squeezing of the tire rubber when it contacts the road, generating heat. Rolling resistance that causes a wheel to slow down when coasting is relatively small compared to the static friction that causes the car to accelerate forward.

Hope this helps.

The static friction between the surface of the tires and the road is actually pushing the car forward.

The "rotational friction", if you mean the kinetic friction of the axle spinning around, is negligibly small compare to air resistance. Rolling friction of the tires is also quite small.

• Yes but there's static friction from the movement itself, shouldn't those frictions cancel each other out. By rotational friction I meant the friction of the movement caused by the rotation of the wheels and the surface. Jul 25, 2021 at 0:12
• that friction doesn't oppose the direction of motion. that friction pushes the car forward. Jul 25, 2021 at 0:24
• there's always friction that opposes movement, no? How else does a car deaccelerate Jul 25, 2021 at 0:29
• Yes - friction always opposes motion between the two surfaces in contact. The surface of a wheel is moving exactly 0mph relative to the surface of the ground when they're in contact. Jul 25, 2021 at 0:29