The Physics of Ice Skating - Angular Momentum

       The angular component of linear momentum is angular momentum. When an object rotates around a fixed axis, the force acting on the object is called the centripital force. This force points inward, toward the center of the circle traced by the rotation. The velocity of the object points tangential to the circle traced. This is illustrated by swinging a ball on a string around your head (don’t hit any lamps though). If the ball becomes detached from the string, it goes flying in a straight line.

       The vector for angular momentum points perpendicular to the velocity and force vectors. It goes according to the “right hand rule.” This is just a simple way of remembering where the angular momentum vector is pointing. Angular momentum is represented by the equation L=I where I equals the moment of inertia and is the angular rotation or the period of rotation divided by 2 . The moment of inertia depends on the mass of an object and also the distribution of that mass around the axis of rotation. So a skater can have a different moment of inertia based on whether their arms are extended or not. This can be compared to linear momentum where p=mv or linear momentum equals mass times velocity.

       Angular momentum is conserved when no outside torques act on an object. As say, the moment of inertia decreases, the angular rotation has to increase to keep the same angular momentum. This is most evident when a figure skater spins. A skater starts the spin with arms outstretched (a large moment of inertia).  As the skater brings the arms in (decreasing the moment of inertia), the rotational speed increases. This is how those incredible spins skaters like Paul Wylie, Todd Eldridge and Kristi Yamaguchi are accomplished. Along with many long years of practice.

       Most of the spins done by world class figure skaters are edge turns, meaning they are spinning while remaining on an edge. For beginners, often the first spin learned is the two-footed spin. A skater rides a large curve with most of their weight on an outside edge. As the curve spirals into the center, the skater rises up on the flats and begins to spin. One of the most important aspects of a spin is how to “center” a spin. This refers to the property that the spin should stay in one place and not travel all over the ice (which is quite hazardous). This requires converting all of the linear momentum into angular momentum. (Another conservation law)

       Another example of conservation of angular momentum occurs when a massive star (meaning several times the mass of our sun) dies. As the star, which is already rotating, begins to collapse, it becomes a smaller sphere which decreases its moment of inertia. Since the star is an isolated system with no forces acting upon it, the angular momentum must be conserved and the rotational period of the star increases. If the star (known now as a neutron star) is emitting a beam of radiation, its rotational motion makes this beam appear to us like pulses. These stars are known as pulsars.

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by Karen Knierman and Jane Rigby