How Do You Go Up in a Swing? |

How do you
like to go up in a swing,Up in the air so blue? Oh, I do think it the pleasantest thing Ever a child can do! Up in the air and over the wall, Till I can see so wide, River and trees and cattle and all Over the countryside-- Till I look down on the garden green, Down on the roof so brown-- Up in the air I go flying again, Up in the air and down! -- Robert Louis Stevenson |

Very likely everyone who ever reads this page will already know

On this page I take a look at a qualitative explanation for the operation of a swing suspended by a single rope or chain on each side. A swing suspended by rigid rods, such as a typical lawn swing, is a little different in its principle of operation, though exactly the same motions will work to get it going.

Throughout this page, I will assume we’re watching someone on a swing from their

Where’s the energy coming from to “pump up” a swing? You can’t give yourself any kind of direct “push”; there is nothing to push

The only place we can reasonably expect to find the energy coming from is gravity. Somehow, at the ends of the arc, when you change position, you must be

But how is this done? Where’s the “lift” coming from?

Note well: Your head and shoulders are

At the back of the arc, you throw your head

Consider what’s going on: At the top of the arc, you are momentarily stationary; in particular, your body is not rotating. Your angular momentum is zero.

At the bottom of the arc, when you’re traveling forward, your body is also

In figure 1, we see a figure on a stationary swing, hanging straight down. The line of pull of the chain is through the center of mass. Gravity, of course, always pulls straight down on the center of mass. So, the figure feels no net torque at that moment.

There are two forces acting on you. Gravity can only pull your center of mass straight down; with your center of mass as the origin, gravity can’t apply a torque to you. So the torque must come from the other force, which is the pull of the chain. It must

Figure 1: |
Figure 2: |
Figure 3: |

To summarize, on the back-swing, you’re rotating clockwise (the “negative” direction). After you pass the low point, you’re slowing down, and so is your rotation. After you pass the peak of the arc in back, you’re rotating counter-clockwise, and your rotation is accelerating. So, throughout the back half of your swing, your angular momentum is increasingly positive, and the pull of the chain must be

To put that differently, everywhere except the bottom of the arc, the pull of the chain is along a line which passes

Figure 4: |

To view it differently, by throwing your head back and feet forward at the back of the arc, you’re “rolling yourself up” in the chain a little bit. In effect, you’re pulling your center of mass up the chain.

The net consequence is that you gain a little potential energy, which comes back as kinetic energy when you swing down. At the bottom of the arc, you’re going faster than you would have been had you not changed position.

At the front peak of the arc, you do the same thing, in reverse, and because the chain is now pulling

Figure 5: |

For all we know, the legend could be true -- for you

As soon as your arc reaches 180 degrees, so that the pull of the chain no longer has a vertical component at the peaks of the arc, the pumping will stop working. There is no way to “pull yourself up” the chain if the chain points

Furthermore, as soon as your arc exceeds 180 degrees, your velocity vector as you near the peak of the arc on the backswing is actually pointing