Acceleration of a point on a disc is as velocity squared, divided by radius. Since velocity of a point on a (rigid) disc is proportional to the radius, this sim

Acceleration of a point on a disc is as velocity squared, divided by radius. Since velocity of a point on a (rigid) disc is proportional to the radius, this simplifies to acceleration being proportional to the radius. Reduce the radius by half, and the acceleration reduces by half. And, at the center, acceleration is zero. (All this, of course, is assuming the angular rotation rate is constant.)