# How does friction causes centripetal acceleration?

1. Feb 20, 2013

### SecretSnow

Hi guys, I'm confused why friction is able to cause centripetal acceleration on a car that is turning in a circular road. Firstly, I think the radial acceleration is provided by the engine alone, and at any point of time the car velocity is tangential to the circular path, and friction is only directly opposing the linear velocity of the car tangentially, and not at right angles to the linear velocity. By the way, the road is totally flat. Shouldn't this be the sole role of friction here? How does it cause centripetal acceleration then? Thanks a lot!

2. Feb 20, 2013

### cepheid

Staff Emeritus
Say you were in a car going in a straight line. Then you decided you wanted to change directions. Without friction, you would turn the steering wheel, and the wheels would turn to one side, but nothing else would happen. You would keep going straight. Why? Because the tires would be able to slide relative to the road, and so now you'd just have sideways facing, forward sliding tires. Friction prevents this sliding motion.

3. Feb 20, 2013

### cepheid

Staff Emeritus
I made this diagram (attached) a while ago, and I think it is a correct representation of the situation at any given instant. The blue vector is the sliding friction I mentioned in my previous post. The red vector is another friction component that comes from the fact that the tires are also spinning, which means that they are pushing back on the road, while the road pushes forward on them (this is another type of sliding motion between tires and road surface that wants to occur).

Add these two friction terms together, and you get the green vector, the resultant. It points centripetally.

#### Attached Files:

• ###### car_turning.jpg
File size:
6.9 KB
Views:
1,234
4. Feb 20, 2013

### rcgldr

There is a Newton third law pair of forces involved, an outwards force that the tires exert onto the pavement, and an inwards force that the pavement exerts onto the tires. The inwards force from the pavement is responsible for the centripetal acceleration of the car. The source of the outwards force on the tires is ultimately due to the reaction of the car's mass to the centripetal acceleration.

5. Feb 21, 2013

### SecretSnow

Thanks guys!! I think I have an idea of how it works but I'm not sure if it's correct. Initially, if the car is traveling straight, the friction is directly opposite to the direction of motion of the wheel but in the direction of the car, forward (which means when the wheels are rolling forward, the direction of friction is in the direction of the motion of the entire car but opposite to the motion of the wheels, which still slows down the car) I imagine that when the car is turning to the left for example, the 2 front wheels first turn left, and this causes the friction to now become in a slanted position against the direction of the wheel motion directly. This slanted friction direction gives rise to both the tangential and radial acceleration of the wheels. This results in both the change in direction of the car towards curving left and also it slowing down. Am I right to say this??

More importantly, I have several questions more. Is friction an indepedent force that exists between the surfaces in contact? Meaning there's no newton 3rd law in place right? Because I think it can't be said that the road exerts a pull on the wheel backwards while the wheel pulls the road forward and this causes friction right??

Another question..friction is rather difficult to present in this context as it is in actuality in the direction of the entire motion of the car, although it resists the motion. This sounds a little contradicting so can I present the direction of friction between the wheels and road overall as against the direction of the whole motion of the car?

Thanks a lot!!

6. Feb 21, 2013

### rcgldr

That's rolling resistance and would still exist even without friction (with lesser magnitude). It's mostly due to the fact that there's more force involved during deformation at the contact patch of a tire, than during recovery from the deformation of the tire, something call hysteresis. There's also some sliding friction at the contact patch due to the contact patch deforming and squirming. Wiki article:

http://en.wikipedia.org/wiki/Rolling_resistance

The friction that allows a car to corner is the same as the friction that prevents a box from sliding even if you push on the box, but not hard enough to cause the box to slide. Even if the box or tires are sliding, the kinetic friction still applies some opposing force in the box case, and still results in centripetal acceleration in the turning car case.

There's always a Newton third law pair for any force. In the case of rolling resistance for a car that is coasting, the Newton third law pair of forces are between the tires and the road. In the case of driven tires of a car at constant speed, the torque applied by the drivetrain to the tires is opposed by the torque related to aerodynamic drag and rolling resistance.

Last edited: Feb 21, 2013
7. Feb 21, 2013

### ehild

There are three kinds of friction involved between the tyres and the rod.

Static friction ensures rolling and also prevents slipping perpendicularly to the velocity. That kind of friction ensures the centripetal force when th ecar travels along a curved track. Without it, a car would slip outward.
Static friction prevents mutual motion of surfaces in contact.

Kinetic friction acts between the slipping tyre and the road.

Rolling resistance means a torque that opposes rotation of the wheels.

ehild