Why does pure translation result in the center of rotation being at infinity?

Pure translation refers to the movement of an object where all its parts move the same distance in the same direction without any rotation. In orthodontics, this concept applies to how teeth move under the influence of applied forces.

When a force is applied to a tooth, if it results in pure translation, the center of rotation is theoretically considered to be at infinity. This is because, in pure translation, there is no tilting or tipping of the tooth. Therefore, any force applied does not cause the tooth to rotate around any fixed point or axis that is within the tooth itself. Instead, the entire tooth moves in the same direction as the force applied, which means that the pivot point (or center of rotation) disappears from a measurable or practical standpoint and is conceptualized as being infinitely far away.

Considering the context, the other choices do not accurately depict the scenario of pure translation. Forces applied at the center of resistance (the first option) may influence movement but do not explain why the center of rotation is infinity. The third option suggests that translation requires no movement, which is not correct; translation is a type of movement. Lastly, the fourth option mentions forces acting on the apex of the tooth but does not relate to the concept of rotation in