The spectacular sight of a figure skater transforming a graceful, measured rotation into a high-speed blur is one of the most compelling moments in sports. The skater begins with arms wide, spinning at a moderate pace, but the instant those arms are drawn inward, the rotational speed visibly and dramatically increases. This sudden acceleration is not achieved through an external push, but rather by manipulating a governing law of physics. The phenomenon hinges entirely on how a body’s mass is arranged relative to its central spinning axis.
The Physics Governing Rotation
The rapid change in a skater’s speed is a perfect demonstration of a fundamental principle concerning spinning objects. This principle states that the total rotational quantity of a spinning body must remain stable unless an outside twisting force, or torque, is applied to it. On the ice, the friction between the skate blade and the ice, as well as air resistance, is extremely low, meaning the external forces acting to change the spin are negligible. Because the net torque acting on the skater is practically zero, their total rotational quantity, called angular momentum, must be maintained. Angular momentum is a combination of the body’s mass, its rotational speed, and how that mass is spread out.
Moment of Inertia: The Role of Mass Distribution
The variable the skater actively controls is known as the moment of inertia, which serves as the rotational equivalent of mass in linear motion. It quantifies the body’s resistance to a change in its rotational motion and is entirely dependent on how the mass is distributed around the axis of spin. When the skater extends their arms and perhaps one leg, the majority of their mass is positioned farther away from the central axis running vertically through their body.
The moment of inertia is mathematically proportional to the square of the distance of the mass from the rotation axis. By having their arms outstretched, the skater maximizes this distance, resulting in a high moment of inertia and a high resistance to spinning quickly.
When the skater pulls their arms and hands inward, bringing them close to the chest, they drastically reduce the average distance of that mass from the center axis. This action immediately lowers the moment of inertia, shrinking the rotational resistance of the body. The difference between arms extended and arms pulled in can reduce the moment of inertia by a factor of three or more, dramatically changing the dynamics of the spin.
Translating Inertia into Speed
The connection between the shrinking moment of inertia and the resulting increase in speed is a direct consequence of the rotational quantity needing to be maintained. Since the total angular momentum is constant, a reduction in the moment of inertia must be balanced by a corresponding increase in the angular velocity, which is the rotational speed. The two factors are inversely proportional: if the moment of inertia is cut in half, the angular velocity must double.
The physical work the skater performs to pull their arms inward drives this transformation, as they are actively moving mass against the outward-pulling forces of the spin. This internal work done by the skater is converted into rotational kinetic energy, which manifests as the increased speed. The speed accelerates until the arms are fully tucked in, at which point the moment of inertia reaches its minimum value, and the spin reaches its maximum rate.
Beyond the Rink
The physical law governing the ice skater’s spin is a universal principle applied across various athletic and natural phenomena. Gymnasts performing twisting somersaults and divers executing flips in mid-air use the exact same technique to control their rotation. By tucking their limbs tightly to their core, they reduce their moment of inertia to speed up their rotation, allowing them to complete multiple revolutions before straightening out for a clean entry. Conversely, an athlete will extend their body just before landing or entering the water to increase their moment of inertia, which slows the spin for a controlled finish. This principle can also be observed when a person sitting on a freely spinning office chair spins faster simply by pulling weights or their legs inward.