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  • Centripetal Acceleration and Radius: Understanding the Relationship
    If you increase the radius of circular motion while keeping the angular velocity constant, the centripetal acceleration will decrease.

    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.

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