Why a figure skater speeds up when pulling their arms in
In short: It is a fundamental law of physics that allows objects to maintain their orientation even while moving through space. By understanding how angular momentum behaves, we can see why certain movements are inevitable and how the universe preserves its own rotational balance.
Angular momentum is a vector quantity that characterizes the rotary inertia of an object or a system of objects in motion about an axis. Because it is a vector, it requires both a magnitude and a specific direction to be fully described. For any system isolated from external forces, the total angular momentum remains constant—a principle known as the law of conservation of angular momentum. This means that unless an external torque is applied, the rate of change of angular momentum is zero.
The calculation of this property depends on whether an object is orbiting or spinning. To calculate an orbiting body's magnitude, one must compute the product of its mass (m), linear velocity (v), and the perpendicular distance (r) measured from the rotation centre to a line aligned with its path (mvr). However, for a spinning rigid object, angular momentum is the summation of that quantity (mvr) for every single particle composing the object. Alternatively, it can be formulated as the product of the moment of inertia (I) and the angular velocity (ω), expressed as Iω.
This relationship explains the classic physics of a figure skater: when they pull their arms inward, they reduce their moment of inertia (I). Since the total angular momentum (Iω) must remain constant in the absence of external torque, the angular velocity (ω) must increase to compensate, causing them to spin faster. This same principle allows tools like gyrocompasses to remain fixed in orientation regardless of an airplane's motion, and it describes both the Earth's daily rotation and its annual revolution around the Sun.
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Sources
- Summary by Intellect · source: Angular Momentum of a System
- Also: Angular momentum | Definition, Examples, Unit, & Facts | Britannica
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