The reason that a gymnast spreads out their arms to stay balanced on a beam, or a tightrope walker carries a long pole, or an ice skater spins faster when they tuck their arms in, can all be explained by the moment of inertia.
The moment of inertia is, basically, how much an object will resist rotation. The higher the object's moment of inertia, the more resistant to rotation the object will be. The general...
The reason that a gymnast spreads out their arms to stay balanced on a beam, or a tightrope walker carries a long pole, or an ice skater spins faster when they tuck their arms in, can all be explained by the moment of inertia.
The moment of inertia is, basically, how much an object will resist rotation. The higher the object's moment of inertia, the more resistant to rotation the object will be. The general equation for moment of inertia is:
`I =int_0^Mr^2dm`
If you're not familiar with integrals, all you need to notice about this equation is that the moment of inertia is dependent on mass (M) and radius from the axis of rotation (r). In order to increase the moment of inertia (and make the object harder to rotate) either the mass or the radius would need to increase. A gymnast obviously can't suddenly increase their mass, but they can spread out their arms to increase their radius.
This relates to the gymnast staying balanced on a beam because when they start to lose their balance, they are essentially starting to rotate around the beam. When they spread out their arms and increase their moment of inertia, they rotate (lose their balance) more slowly thus making it easier to correct their position on the beam.
This is exactly the same reason that the long pole helps a tightrope walker keep their balance. An ice skater, on the other hand, spins faster when their arms are tucked in because it decreases their moment of inertia making them less resistant to rotation.
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