In the scenario you described, where two individuals are positioned at different distances from the center of a rotating disk, and the disk is rotating at speeds close to the speed of light, there will indeed be a time dilation effect. However, the effect will not result in one person being younger and the other older.
The time dilation effect that arises in this scenario is a consequence of both the rotational motion and the relativistic effects of special relativity. As an object or observer moves faster, time appears to pass more slowly for them relative to a stationary observer. This is known as time dilation.
In the case of the rotating disk, the points closer to the center are rotating at a slower linear speed compared to the points farther from the center. Therefore, the observers at the outer edge of the disk are moving faster in terms of linear velocity and will experience a greater time dilation effect relative to the observers closer to the center.
However, it is important to note that this effect alone does not result in one person being younger or older than the other. The time dilation effect only applies to the local experience of time for each observer. Each person on the rotating disk will perceive their own clock to be running normally. The perceived time differences will arise when they compare their experiences with each other or with an external reference frame.
If the observers on the rotating disk were to measure their ages and compare them after a period of time, they would find that each person's clock has ticked the same number of times. They would not find one person significantly younger or older than the other due to their relative positions on the rotating disk.
In summary, while there will be a time dilation effect due to the different speeds of rotation on the disk, it will not result in one person being younger and the other older. Time dilation effects depend on relative motion and are not sufficient to create significant age differences between individuals in this scenario.