When an ice skater glides onto the ice, spins gracefully, and then suddenly pulls their arms inward, a remarkable change occurs. Their rotation visibly accelerates, transforming a gentle turn into a rapid blur. This visible acceleration showcases a fundamental principle of physics.
Understanding Angular Momentum
Angular momentum is a physical property that describes an object’s tendency to continue rotating. This property is a combination of how much mass is rotating, how quickly it is spinning, and how that mass is distributed relative to the center of rotation. Just as linear momentum describes an object moving in a straight line, angular momentum applies to objects that are rotating or revolving.
A central concept related to angular momentum is its conservation. In a system where no external twisting force, known as torque, is applied, the total angular momentum remains constant. For an ice skater, the friction from the ice and air resistance are minimal, making them an excellent example of a system where angular momentum is largely conserved during a spin.
The Role of Mass Distribution
An object’s resistance to changes in its rotation is quantified by a property called “moment of inertia.” This value depends on both the object’s total mass and, more importantly, how that mass is spread out around its axis of rotation. If mass is concentrated close to the center of rotation, it is easier to start or stop its spin. Conversely, if mass is distributed farther from the center, the object will resist changes in its rotation more significantly.
An ice skater manipulates their moment of inertia during a spin. When a skater extends their arms and legs, they distribute their body mass farther from their central axis of rotation, which results in a larger moment of inertia. When they pull their arms and legs in close to their body, they bring their mass closer to the axis of rotation, thereby decreasing their moment of inertia. This change in mass distribution directly impacts how readily their rotational speed can change.
Why the Skater Speeds Up
The dramatic increase in an ice skater’s spin speed when they draw in their arms is a direct consequence of the conservation of angular momentum and the change in their moment of inertia. As the skater spins, their total angular momentum remains constant because there is minimal external torque acting on them. This constant angular momentum is a product of their moment of inertia and their angular velocity, or spin speed.
When the skater pulls their arms inward, their mass distribution shifts closer to their axis of rotation, causing their moment of inertia to decrease. Since angular momentum must remain unchanged, a decrease in moment of inertia necessitates an increase in angular velocity. To compensate for the reduced resistance to rotation, the skater’s spin speed must increase proportionally. This adjustment occurs naturally without any external force making them spin faster; it is simply a redistribution of their own mass influencing their rotational motion.
Everyday Examples of Angular Momentum
The principle of angular momentum conservation extends beyond ice skating and can be observed in various everyday situations. Divers demonstrate this principle during their acrobatic maneuvers. After launching from a springboard, a diver can increase their somersaulting speed by tucking their body into a compact ball, reducing their moment of inertia. They then extend their body before entering the water to slow rotation for a smooth entry.
The “cat righting reflex” is another example. A falling cat can reorient itself in mid-air to land on its feet, even if it starts with no initial rotation. It achieves this by changing its body shape, rotating different parts of its body in opposite directions to alter its moment of inertia and achieve a net rotation. Planets orbiting the sun exhibit this principle; they move faster when they are closer to the sun and slower when they are farther away, as their orbital angular momentum remains constant.