Here's why:
* Centripetal acceleration formula: a = v²/r
* 'a' is centripetal acceleration
* 'v' is the linear velocity
* 'r' is the radius of the circular path
* Relationship between linear and angular velocity: v = ωr
* 'ω' is the angular velocity (radians per second)
Combining these equations:
* a = (ωr)² / r
* a = ω²r
This shows that centripetal acceleration is directly proportional to the radius when angular velocity is constant.
Therefore, if you increase the radius, the centripetal acceleration decreases.