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This video shows someone climbing a ladder not resting against a wall: https://youtu.be/bWOSbEtDAas . I was wondering if it's harder to balance the ladder when you're standing near the bottom, or standing near the top.

Intuition for why it might be easier near the bottom: the ladder tipping has less effect on your body's center of mass.

Intuition for why it might be easier near the top: climbing the ladder increases the moment of inertia of the you+ladder system. Analogy: it's easier to balance a vertical rake on the palm of your hand than it is to balance a vertical pencil.

Craig Gidney
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At the bottom. You will begin to fall as soon as the center of mass of the system passes through the vertical plane of the legs of the ladder. As you point out, this happens more easily up high by simple geometry.

You also mention a higher moment of inertia associated with being up higher. This is true, but really only means that, as you fall, you accelerate slightly slower than you would have had you been lower.

Consider a similar situation, which is easier: walking in platform shoes elevated 1cm or 1m?

In response to the rake vs pencil: here you are able to move the support point so the slower fall from the higher moment of inertia is very helpful. When balancing on a ladder, you can only lean your weight from the top.

bRost03
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