Implement equals (and hashCode) in Object1 class based on idNum field, then you use List.indexOf
like this
int i = objList.indexOf(new Object(idNum));
or make a special class for seaching
final String idNum = "1";
int i = list.indexOf(new Object() {
public boolean equals(Object obj) {
return ((X)obj).idNum.equals(idNum);
}
});