Here's why:
* Linear speed refers to the rate at which an object moves in a straight line.
* Angular speed refers to the rate at which an object rotates.
While the disc is rotating, you are rotating with it. However, since you are at the center, you are not moving in a straight line. You are essentially stationary relative to the disc's center.
Therefore, your linear speed is zero, even though you have a non-zero angular speed.