Is there any Issur for a child to use a swing at a playground on Shabbat? (no Eruv) Is there any Issur in an adult pushing a child on a swing? In either case, which Av Melacha does it fall under if Assur?
Pushing a child on a swing is allowed. Since it does not involve picking up the child from a stationary position and then depositing the child in another stationary position, it is not carrying.