Centripetal and Centrifugal Forces in Sport

From Newton’s Law of Inertia we know that objects will continue to move in a straight path unless compelled by force to do otherwise. It follows, therefore, that when an athlete spins with a hammer (to take the best of countless examples in athletics) he must apply force to keep it moving in a near circular path.

By exerting this force—by pulling on the hammer—he accelerates it, even if it continues to move with only uniform speed, for by changing the hammer’s direction of motion he is continually changing its velocity. But as soon as he lets go, the hammer continues steadily along at a tangent; its inertia makes it move in a straight line again, at right angles to the radius of motion at the point of release.

The pulling-in force exerted by the athlete is called centripetal, the equal but opposite reaction to which is a centrifugal force, acting on the athlete, pulling outward directly along the radius of motion. Speaking generally, in athletics this centrifugal force is a by-product of an effort to increase rotational speed; in itself it is seldom advantageous and is more often an embarrassment to an athlete.

The force required to keep an object moving in a circular path (and the equal but opposite centrifugal force) depends upon the mass and speed of the object and its radius of motion. Other things being equal, this force (i) is proportional to the moving mass. Thus, a 16-lb hammer is pulled in (and, therefore, outward simultaneously) with twice the force of an 8-lb one; (ii) is proportional to the square of the velocity. If the hammer’s speed (i.e. the actual, linear speed) is doubled, the centripetal and centrifugal forces increase four-fold. That is to say, it is proportional to the square of the velocity (i.e. the angle described by the hammer per second). For example, if angular velocity is increased three-fold then the hammer needs nine times the original force to be kept moving in a circular path, to which the reaction is nine times the original centrifugal force; (iii) for a constant angular velo city, is proportional to the radius of motion. Again, with hammer throwing as our example: when two men turn with the same an gular velocity, the shorter man, with half the radius of motion of the taller, needs only half the centripetal force (and, therefore, half the centrifugal force) to control it.

During certain phases of the hammer-turns, when both man and hammer-head are spinning with equal angular velocity, their respective distances from the axis are inversely proportional to their masses; i.e. if the athlete weighs sixteen times as much as the hammerhead, his radius, relatively, will be sixteen times less (the measurements being made along each radius from the axis to each Centre of Gravity). Under such circumstances the centripetal force pulling on the hammer is equal to the centrifugal force pulling simultaneously on the athlete, but in an opposite direction.

Since almost all athletic movement is angular in character, these prin- ciples apply to greater or lesser degree in all events. However, they have a particular significance in hammer and discus throwing and in the pole vault.

They apply, too, to bend-running, where athletes find it more difficult to sprint at top speed in an inside lane than in an outside one.

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