Problem data: an1 (initial centripetal acceleration) = 9an2 (final centripetal acceleration), the radius of rotation of the conditional body will be considered constant.
The change in rotation frequency with a decrease in centripetal acceleration is determined from the ratio (the basic formula is an = 4 * Π ^ 2 * R * ν ^ 2): ν1 / ν ^ 2 = √ ((an1 / (4 * Π ^ 2 * R)) / (an ^ 2 / (4 * Π ^ 2 * R))) = √ (an1 / an2) = √ (an1 / (9an1)) = √ (1/9) = 1/3.
Answer: The rotation frequency will decrease by 3 times.
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