# How is it possible that friction = centripetal force for turns?

• x86

#### x86

So, I am confused. If a car is driving on a flat surface and it turns, it experiences centripetal force. Apparently, the friction of the bike is equal to this force. This doesn't make sense to me. I've drawn a few forces on an example picture here:

The car is going straight, and Fa is the force applied going straight (and friction in the opposite direction). The car then suddenly turns and its tires are perpendicular to its old direction.

I can only see four forces acting now:
1. Fa as depicted
2. Ff as depicted
3. Fi as depicted, which is in the new direction the tire is rolling towards.
4. Another frictional force acting in the same direction as Fi, which is going against the tire motion

The only problem is that this frictional force acting in the same direction as Fi is only affecting the tires, its slowing them down and shouldn't affect centripetal force. Its not actually accelerating toward the center of the circle, all it is doing is slowing down the tires.

So how come people say Ff = Fc for turns on flat roads? It doesn't make sense for me.

I can solve the problems easily, as I know the theory, but I just can't understand it for this specific scenario.

If we say that Ff = Fc, then how come we can't say that when a car is driving, the frictional force is actually in the direction that it is driving in (because of the tires).

Therefore, there would be two forces acting on the car.

1. The force making it go forward
2. Friction also making it go forward; but only affecting the tire speed.

Therefore, in freebody diagrams; if we are to follow the Ff=Fc logic, why do we draw it so frictional force is directed in the motion opposite of a car, when it really isnt? Is it just to make it easier for people to follow, since it is, after all, affecting the tires motion? (According to the Ff=Fc logic for this example)

What? You don't think tires won't develop friction if they start moving sideways to the direction of travel?

What? You don't think tires won't develop friction if they start moving sideways to the direction of travel?

Yes there will be friction, but the friction won't be toward the center of the circle.

Yes there will be friction, but the friction won't be toward the center of the circle.

The physics of a car in a turn are surprisingly complex (which is why the people who build race cars are always redesigning and tweaking suspensions) but there's a simple model that works pretty well if the tires are holding so the car isn't skidding:

The tire contact patch, the part that's touching the ground, is not moving relative to the ground even though the tire is rolling; as the tire rolls it picks up the back of the patch and pushes more rubber down onto the road at the front of the patch. If you imagine a bug riding on the tire... The bug will be squashed flat but it won't be smeared sideways as the tire rotates.

OK, so at any given moment the tire contact patch is at rest relative to the surface of the road. Static friction stops it from sliding (if it did slide, we'd be skidding, not turning). We turn the steering wheel so that the contact patch moves to follow the curve. However, the car is still moving in a straight line under the influence of inertia so the tire sidewalls stretch as the contact patch moves away from a straight line while the wheel/axle tries to follow a straight line. Of course the tire resists this stretching, so it exerts a force on the wheel/axle... And this force is pretty much directly oriented towards the center of the turn.

What I think happens is in the attachment.

#### Attachments

• wheel.png
5.4 KB · Views: 1,065
The vector sum of Ff and the force labeled as 4. in the original post has a direction towards center and its the centripetal force.

What confuses you is that Fa and Fi are fictional forces (not fRictional) and they don't really exist. Friction forces are the only ones that give translational acceleration to a car. The forces from the engine pistons all they do is to give rotational acceleration to the wheels.

Just to be clear I understand the orginal post and that the original poster understands the issues:

The force that opposes tire rotation is called rolling resistance, not friction. It's mostly due to the inelastic deformation that occurs at the contact patch, where the force during recovery is less than the force during deformation, converting mechanical energy into heat.

If a car is not accelerating, then there's only enough static friction to overcome rolling resistance.

If a car is turning at constant speed, then the only acceleration is centripetal and related to the normally static (non-sliding) friction at the tires. There's a Newton third law pair of forces at the contact patches: the tires exert an outwards force onto the pavement, and the pavement exerts an inwards force (the centripetal force) onto the tires.

I have to ask myself, what force other than friction is available to provide the centripetal motion? You surely have to fit your explanation to the facts and not the other way round.

In classical textbook examples, the static friction force is used to neutralize some other force, and both two forces will vanish when we calculate the net force. For example, when we slightly push a book on the table, the book will not move because our push is neutralized by the static friction force. The total net force is zero, both forces vanish (i.e, they cancel out).

However in this thread's situation, this static friction force does NOT vanish but remains and becomes the centripetal force – that's also the NET force.

Therefore, I personally think that to fully understand the situation, one needs a more correct definition of the static friction force in the first place.

In classical textbook examples, the static friction force is used to neutralize some other force, and both two forces will vanish when we calculate the net force. For example, when we slightly push a book on the table, the book will not move because our push is neutralized by the static friction force. The total net force is zero, both forces vanish (i.e, they cancel out).
Summing forces to zero doesn't make them vanish. Pick up a heavy weight and hold it for a while to make sure you can see that.

Summing forces to zero doesn't make them vanish. Pick up a heavy weight and hold it for a while to make sure you can see that.

Yes, they do not vanish. But I mean they cancel out and thus they don't appear in the net force calculation.

However, in this situation, the static friction force is the net force. It would have been canceled out by some other forces, if we think of the static friction force's behavior as in the classical example I mentioned above.

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In the case of a car tire during a turn, the front wheels (and tires) are actually pointed slightly "into" the turn, and that's actually what causes the car to rotate.

In a steady turn, (to some approximation) you could consider the front and rear tires to be angled so that all wheels are pointed tangentially, and the friction force is inward radial.

I have to ask myself, what force other than friction is available to provide the centripetal motion? You surely have to fit your explanation to the facts and not the other way round.

To put that another way, centripetal force is generated whenever an object in motion is acted upon by a force that changes its direction. It is the friction that creates the centripetal force, by changing the direction of motion. It is turning the steering wheel that creates the friction, as much or little as the driver demands, subject to the limits imposed by the coefficient of friction... characteristics of the tire and the road. Perhaps it would help to point out that when the car is at rest, or moving straight and steady, there is negligible friction between tire and road. That's what makes the wheel useful.

Friction is the force that resists the relative motion of objects in contact. No relative motion, no friction. Demonstration: Hold a match firmly against the side of a matchbox.

Wait for it to light. Keep waiting. And waiting. And waiting... until you get bored.

Now, rub the match across the side of the box.

It was the relative motion, mutual pressure and coefficient of friction that created the friction force that created the heat that lit the fire.

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Velocity has components speed and direction. If the direction is changing (because car is moving in a circle) then it is accelerating. To accelerate there must be a net force. It's provided by friction.

Friction is the force that resists the relative motion of objects in contact. No relative motion, no friction. Demonstration: Hold a match firmly against the side of a matchbox.

Wait for it to light. Keep waiting. And waiting. And waiting... until you get bored.

Now, rub the match across the side of the box.

It was the relative motion, mutual pressure and coefficient of friction that created the friction force that created the heat that lit the fire.

You're confusing force and energy. Only when there is relative motion energy can be converted to heat, but there can be a force without relative motion. Consider the forces on a car parked on an incline. They won't balance without friction.

No relative motion, no friction.

That's not right. Consider a fridge magnet. Friction force stops it falling but there is no relative motion.

Yes there will be friction, but the friction won't be toward the center of the circle.

Why not?

If it doesn't point towards the centre there will be a component that tends to slow or speed up the car. Draw it.

If the force is in any other direction it won't be moving around a circle at a constant speed.

That's not right. Consider a fridge magnet. Friction force stops it falling but there is no relative motion.

You're confusing force and energy. Only when there is relative motion energy can be converted to heat, but there can be a force without relative motion. Consider the forces on a car parked on an incline. They won't balance without friction.

A magnet stuck to a fridge is not at rest. It's just stuck. A car parked on an incline is not at rest. It's just parked. I specifically mentioned that.

And to emphasize, Friction is the force that Resists relative motion between objects in contact.

It can do so successfully. When that happens, it is called static friction. When static friction is exceeded, and the objects actually move, it is called kinetic friction.

Friction is equal to or less than the product of the forces objects impose on one another and the friction coefficient. In the case of the magnet, magnetic force times the friction coefficient exceeds the influence of gravity, therefore, no motion. In the case of the car parked on an incline, the pressure of brake shoe on steel times the friction coefficient exceeds the influence of gravity, therefore, no motion. If the magnet, or car, moving or parked, was on a more slippery surface the friction coefficient might be low enough that static friction is exceeded. In which case there would be relative motion between the objects, and kinetic rather than static friction.

In the alternative case of the magnet being stuck to the top of the fridge, or the car parked on a level patch of ground, or the moving car is traveling straight, that is to say, when objects in contact are at rest with respect to one another, the absence of a relative motion impulse equates to an absence of friction. Because there is no relative motion for friction to resist. Even though the other forces are the same (or, in the case of the magnet, greater) and so is the friction coefficient.

Having said all that, I note that my example was not entirely clear. And not well received. I will try to do better next time.

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A magnet stuck to a fridge is not at rest. It's just stuck. A car parked on an incline is not at rest. It's just parked.
You seem to have a strange concept of "rest".

You seem to have a strange concept of "rest".

Not at all.

A car on a hill will roll down the hill. It is the brake, acting continuously, that prevents the car from rolling.

A magnet stuck to a fridge would, if not for the magnetic force, fall to the floor.

In both cases friction, STATIC friction... acts continuously to prevent motion that would otherwise occur. An object held in place by a force is stationary. But being at rest means it stays where it is without applying a force to keep it there.

That is not an accurate definition of "at rest". I don't know who told you that, but it's incorrect.
An object at rest will remain at rest unless acted upon by an unbalanced force.

Saying that an object needs to be completely devoid of forces to be at rest is ridiculous.

Saying that an object needs to be completely devoid of forces to be at rest is ridiculous.
Yeah, now I can't even have a rest on my bed.

Travis. A.T.

Please pick up a bowling ball. Hold it at arms length, head high.

Now, rest.

Does it not upon due examination turn out that YOU, yes YOU, were holding the ball up?

And what happened to the ball? Did it not achieve of it's own volition the lowest potential energy state available to it?

And what exactly is your quibble?

Frosted, your semantics are irrelevant. The physical concept of an object being at rest is simply that it does not move. It may be used in slightly different ways outside of physics, but within physics, this is not negotiable - it is simply the way it is used.

Well then. You better forget everything I said.