*624In two related child protective proceedings pursuant to Family Court Act article 10, the father, Sefíja V, appeals, as limited by his brief, from so much of two orders of disposition (one as to each child) of the Family Court, Queens County (Hunt, J.), both dated June 24, 2002, as, upon fact-finding orders of the same court dated February 28, 2002, made after a hearing, finding that he abused Sanel V and derivatively neglected Dilaela V, placed the children in the custody of the father and the mother under the petitioner’s supervision for a period of 12 months, and the mother, Murdija V, separately appeals, as limited by her brief, from so much of the order of disposition pertaining to Dilaela V as was based upon that part of the fact-finding order dated February 28, 2002, as found that she derivatively neglected Dilaela V, and from stated portions of the order of disposition pertaining to Sanel V
Ordered that the appeals from those portions of the orders of disposition that placed the children in the custody of the father and the mother under the petitioner’s supervision for a period of 12 months is dismissed as academic, without costs or disbursements, as those portions of the orders of disposition have expired by their own terms; and it is further,
Ordered that the order of disposition pertaining to Sanel V is affirmed insofar as reviewed, without costs or disbursements; and it is further,
Ordered that the order of disposition pertaining to Dilaela V is modified, on the law, by (1) deleting the provision thereof finding derivative neglect of Dilaela V by the mother, and the proceeding pertaining to Dilaela V against the mother is dismissed, and (2) deleting the provision thereof finding that derivative neglect of Dilaela V by the father was established pursuant to the allegations of count seven of the petition and substituting therefor a provision finding that derivative neglect of Dilaela V by the father was established pursuant to the allegations of count two of the petition; as so modified, the order of disposition pertaining to Dilaela V is affirmed insofar as reviewed, without costs or disbursements, and the fact-finding order is modified accordingly.
The appeals from so much of the orders of disposition as placed the children in the custody of the father and the mother under the petitioner’s supervision for a period of 12 months must be dismissed as academic because those portions of the *625orders have expired by their own terms (see Matter of Ziaire M., 309 AD2d 938 [2003]). However, the adjudications of abuse and derivative neglect have not been rendered academic (see Matter of Ciara M., 273 AD2d 312, 314 [2000]).
The Family Court properly determined that the father abused Sanel V (hereinafter the son). The petitioner, Administration for Children’s Services (hereinafter ACS), established by a preponderance of the evidence that on the night of the incident the father intentionally inflicted physical injury upon the son which created a substantial risk of impairment to his physical health (see Family Ct Act § 1012 [e] [i]; § 1046 [b] [i]; Matter of Mayabelle F., 5 AD3d 768 [2004]; Matter of Pierre M., 239 AD2d 262 [1997]; Matter of Angelique H., 215 AD2d 318, 319 [1995]; Matter of John G., 89 AD2d 704 [1982]; cf. Matter of Jason T., 2 AD3d 738, 739 [2003]; Matter of Rosina W., 297 AD2d 639, 640 [2002]; Matter of Amanda E., 279 AD2d 917, 918-919 [2001]).
The Family Court’s finding that the father derivatively neglected Dilaela Y. (hereinafter the daughter) was likewise supported by a preponderance of the evidence. “Evidence of the physical abuse of one child logically supports the conclusion that the parent [has] a faulty understanding of the duties of parenthood and that [the] other child is therefore neglected because there is a substantial risk that his or her mental, emotional or physical condition is in imminent danger of becoming impaired by the infliction of excessive corporal punishment” (Matter of Christina Maria C., 89 AD2d 855 [1982]; see Family Ct Act § 1012 [f] [i] [B]; § 1046 [a] [i]; Matter of Brittney C., 242 AD2d 533, 534 [1997]). The Family Court mistakenly made the finding of derivative neglect of the daughter by the father under count seven of the petition, which alleged derivative neglect of the son, rather than under count two, which alleged derivative neglect of the daughter. We correct this technical error by amending the fact-finding order pertaining to the daughter.
However, as the petitioner correctly concedes, the Family Court’s finding that the mother derivatively neglected the daughter is unsupported by a preponderance of the evidence. “A finding of neglect . . . cannot be sustained in the absence of evidence that the parent or guardian knew or should reasonably have known that the child was in imminent danger of becoming a victim of . . . physical, emotional, or mental impairment” (Matter of Sara X., 122 AD2d 795, 796 [1986]; see Matter of Christina P., 275 AD2d 783, 784 [2000]). Family Court Act § 1012 (f) (i) (B) provides that a parent has neglected his or her child where the parent allows the child to be harmed or placed in substantial risk of harm (see Matter of Krystin M., 294 AD2d *626577 [2002]). Furthermore, there must be a willful omission in the protection of the child by the parent (see Matter of Sara X., supra; Matter of Christina P., supra). The Family Court’s finding that the mother derivatively neglected the daughter cannot be sustained (see Family Ct Act § 1012 [f] [i] [B]; see generally Matter of Brittney C., supra; Matter of Christina Maria C., supra).
The parties’ remaining contentions are without merit. Altman, J.P., Goldstein, Adams and Crane, JJ., concur.