A Prince William County man was convicted of second degree murder yesterday in the death of 4-year-old Rodney Williams, who died after authorities were warned repeatedly of abuse.

Prince William Circuit Court Judge Arthur Sinclair found Carroll Leon Cole, 24, of Dale City guilty after finding "compelling" evidence that Cole's abuse of the child caused his death. He could be sentenced to up to 20 years in prison for second-degree murder, defined as murder without premeditation. Sentencing was set for April 6.

Rodney's death last Sept. 10 generated support in the Virginia General Assembly for a law that would require county welfare agencies to disclose to prosecutors records of serious child abuse cases. The measure has been approved in the House of Delegates and awaits action in the Senate, according to Prince William Commonwealth's Attorney Paul Ebert.

It was disclosed at legislative hearings that as early as August 1976 Prince William social service authorities were aware of abuse against Rodney and that they failed to disclose their records to police on privacy grounds.

The chief witness against Cole at this trial was Gloria Williams, 23, Rodney's mother, with whom Cole formerly lived.

Testimony from her and from Fairfax County Medical Examiner Dr. James C. Byer showed that the boy died after suffering multiple injuries, including buttock burns, from being forced to sit in scalding water and bruses caused by beatings with a length of cord. Rodney's mother testified the injuries were inflicted as punishment for bed wetting.