When a car turns, how does the cornering force from the road change direction?

Question

The road does not change the direction of the force on the cornering wheel because the road is static. That means the wheel must apply the force to the road and the cornering/turning force is a reaction force. So we are left with the wheel changing direction which results in the changing road cornering force direction.

So what changes the direction of the wheel?

-If we say the cornering force changes the wheel direction then we have a wheel that no longer creates a cornering force because the cornering force and wheel rolling direction, at any instant, are always perpendicular.

-Similarly, if we say the wheel changes direction because the car is in circular motion - having direction changing angular momentum - then that ignores the fact that the wheel applies the force and the cornering force is a reaction force. The cornering force is what changes the velocity direction and not the wheel rolling direction.

-If we say the cornering force always exists because the wheel rolling direction and velocity direction (direction of motion) are not aligned then we are saying that the cornering force never changes the velocity direction.

Answer 1

If you do not have a cornering force, then the wheel would go on in a straight line. So in order to turn, you need this force, and it is exerted by the road on the wheel.

How does this force arise? Well you get it by rotating the wheel relative to its current direction.

When the wheel is going straight, and you have free rolling, there is no friction, just the wheel spinning. When the wheel is actuated under an angle, then this angular direction is now the direction in which there is no friction. In the absence of forces, the wheel would still want to keep moving in its original direction. However, the road all of a sudden can now exert a friction force on the wheel.

What direction can this force act in? Only normal to the wheel, since the spinning direction is essentially friction free. This is generating the cornering force. It's the friction caused by the misalignment of the wheel with respect to its instantaneous direction of motion.

Note that you need a force to turn the wheel, otherwise the wheel would want to self-align. This is called self-aligning torque. This is why, when you have a coin spinning in a circle, it needs to be angled inwards a bit, so that gravity can generate this force.

Answer 2

First you have the wheels on the car. We can consider wheels as devices that give us arbitrarily low forces in one direction (perpendicular to the axis when the wheel is rolling) and arbitrarily high friction parallel to the axis.

Next you have a vehicle with two axles, where the front axle and rear axle are at an angle.

As the car is rolling, this creates forces at different points on the car, which becomes a torque. If we imagine the car is rolling forward with the front wheels to the left, frictional forces arise that force the axle to the left.

This unbalanced force on the front of the car has two effects:

• Accelerates the car to the left
• Turns the car in the leftward direction.

Assuming the wheel angle is held constant by the steering mechanism, this continues as the car moves forward. The car is constantly accelerated to the left (in the car's reference frame), but the turning of the car changes the angle so the car moves in a circle rather than accelerating off in one direction.

(Once the car begins turning, the torque is zeroed out by the rear wheels. If the rear wheels did not do this, the car would spin rather than turn)

Why does it move in a circle? Why does the wheel change rolling direction? Why does the force from the road change direction?

We are assuming there is some mechanism that holds the "turning" wheels (the front wheels on a normal car) at some angle to the body. In the normal case, it is the driver holding the steering wheel at some angle. We could replace this with a block of wood where the front wheels are locked at some angle.

With this true, the torque on the vehicle is transmitted to the driving wheel, turning it at the same rate. This modifies the direction of the force applied by friction. As it is always parallel to the axle, the direction is changed as the car moves forward.

The consequence of this is that if the forward speed is constant, the magnitude of the friction (and therefore the acceleration and torque) are also constant.

A force/acceleration that is perpendicular to the direction of motion (which is what an ideal wheel does) will create circular motion.

It seems like you are looking for some part of this to be connected, but I'm not sure what part that is.

• The wheel generates a force (due to friction) parallel to the axle.
• The direction of the force is determined by the orientation of the wheel.
• The wheel's orientation is fixed (for this problem) with the body of the car.
• The car turns because of torques from the front and rear wheels.
• A force that is applied perpendicular to motion creates (in certain cases) circular motion.