|MadSci Network: Physics|
The energy that is being put into the system comes from the body of the person swinging. What your little girl is doing is to generate angular momentum with her legs at the ends of her oscillation, which she transfers to the swing by means of forces she applies with her arms and seat. Since these two forces do not act in line with each other, they create a torque on the swing. This torque, applied mostly at the ends of the oscillation, will add energy just like a push. Since the swing will store energy, these little additions will pile up, and the swing goes higher. The torque that she uses to move her legs comes from the force the swing applies to her, which is not in line with the axis of the legs (her knees). Try swinging yourself, but this time try to feel what is happening and apply your physics to it. Feel where the swing is pushing on you and where you are pushing on the swing. It is also possible for someone swinging to get started all by themselves (without pushing off of the ground) by just "pumping". You might have your little girl try this sometime; it takes some determination.
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