Mud Water splashing off the tyre is due its Centrifugal force:
An object traveling in a circle behaves as if it is experiencing an outward force.
This force, known as the centrifugal force, depends on the mass of the object, the speed of rotation, and the distance from the center. The more massive the object, the greater the force; the greater the speed of the object, the greater the force; and the greater the distance from the center, the greater the force.
It is important to note that the centrifugal force does not actually exist. We feel it, because we are in a non–inertial coordinate system. Nevertheless, it appears quite real to the object being rotated. This is because the object believes that it is in a non–accelerating situation, when in fact it is not. For instance, a child on a merry–go–round is not experiencing any real force outward, but he/she must exert a force to keep from flying off the merry–go–round. Because the centrifugal force appears so real, it is often very useful to use as if it were real.
The more massive the object, the greater the force. We know that this is true because an adult will have a harder time staying on a merry–go–round than a child will. The greater the speed of rotation, the greater the outward force. We know that this is true because a merry–go–round is harder to stay on, the faster it rotates. If you move further out on the merry–go–round, you will have to exert a greater force to stay on. In order to stay on a circular path, we must exert a force towards the center called centripetal (or “center–seeking”) force.
Consider a rope with a ball on the end. You can swirl the ball around in a circle over your head while holding onto the rope. The ball experiences the so–called centrifugal force, and it is the rope that provides the force to keep in moving in the circle.