Is it possible to do a loop on a swing

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First, I will calculate how fast you need to go at the bottom of the swing in order to be able to make a complete loop without the rope going slack. Next, I will estimate whether you can achieve this speed by "pumping" - that is, moving your center of gravity around to increase your speed. The velocity you need can be determined from the length of the swing.

And in order to have sufficient acceleration to counter gravity, you need a speed to keep the rope taut:. Note - this does mean that you will feel significant g forces at the bottom of the swing Don't try this with your toddler!

In principle this only depends on the friction forces on the swing, and how much energy you can add per "pump". However, I think in practice the answer will be "no" - and here is why:. The action of "pumping" on the swing is basically an application of conservation of angular momentum. By moving your center of mass closer to the center of rotation, you increase your velocity.

There is a very nice explanation of this in this answer. The key on a swing is that you "pump" near the bottom of the swing, when it is going fast; and you "release" when you get to the end of the swing where your velocity goes to zero.

Normally, you move just a short distance, and add just a little bit of energy. But to make a full loop, you need to add sufficient energy in a single "pump" to go all the way around. This is the most you can swing without the rope going slack unless you do a full In this case, the velocity at the bottom of the arc is.

You can do this if you can move your center of mass closer to the center of rotation.