Does the direction of the torque acting on a car tire change depending on which direction the tire is rotating?

Question

As I understand, the reason why unbolted car tires will fly off perpendicular to the direction of a moving car is because of the torque generated by the axel. This is unintuitive to me because there isn't an apparent force that would be acting on the tires in that direction, but I understand the math of it at least.

My question is: If I unbolted the tires and observed that all 4 tires would fly off the car when moving forward, can I assume that reversing directions (going backwards) would create torque in the opposite direction, keeping the tires attached to the vehicle?

If not, why isn't this the case? An answer that uses math would be appreciated.

Answer 1

car tires will fly off perpendicular to the direction of a moving car

I'm not sure this is true. I've seen cases where they move in about the same direction the car was.

because of the torque generated by the axel.

Note that torque is an axial, or pseudovector. From the link

A pseudovector (or axial vector) is a quantity that behaves like a vector in many situations, but its direction does not conform when the object is rigidly transformed by rotation, translation, reflection, etc.

In the case of torque $$\mathbf\tau=r\times \frac{dp}{dt}$$ the vector $\bf\tau$ points along the direction of changing angular momentum.

If not, why isn't this the case?

More accurately, the exact direction wheels would fly off would depend on a combination of complicated forces, vibrational motion and cyclical stresses. But because of momentum (linear and angular), you'd expect that most of the times, the wheel's would continue in the approximate line of motion of the car's original direction.

If I unbolted the tires and observed that all 4 tires would fly off [perpendicular to the direction of] the car when moving forward, can I assume that reversing directions (going backwards) would create torque in the opposite direction

No, for the reasons stated above.