Biomechanics and the Olympics: Part IV

Many different Olympic sports involve rotational motion of the entire body, with the most popular probably being diving and gymnastics (trampoline too, that is crazy!).  When we examine motion, one of the first things we have to look at is the inertia of the object or the person.  Inertia is resistance to change in motion, and is measured by an object or a person's mass.  The greater the inertia of an object or person, the greater the force that is required to start, stop, or change the object or person's motion (this is Newton's first law of motion; objects in motion stay in motion and objects at rest stay at rest unless acted upon by an outside force).  For example, if you were going to lift a 25 kg block off the floor and a 50 kg block off the floor, it would take more force to lift the 50 kg block, because it is more massive and has more inertia.  The force applied to an object or person has to be greater than its inertia in order to cause a change in motion.  When we examine rotational motion, such as the flips, tucks, twists, and spins that occur in diving and gymnastics, we have to consider the mass moment of inertia of the person.  The mass moment of inertia is resistance to change in rotational motion, and is the mass of the person and the way the mass is distributed about the axis of rotation.  In these rotational motions, we can consider the axis of rotation to be the center of gravity.  The further away from the axis the mass is located, the greater the mass moment of inertia, and the closer to the axis the mass is located, the smaller the mass moment of inertia.  When the divers and gymnasts want to increase their rotational velocity, they get into a tucked position, such as in the picture above.  This brings the athlete's mass towards the axis of rotation, and reduces the mass moment of inertia.  When the athlete wants to slow down and decrease their rotational velocity (when they are about to enter the water or land), they come out of a tucked position into a more extended position (in the picture below), which will increase their mass moment of inertia and reduce their rotational velocity.  The same principle is demonstrated with figure skaters; when they want to rotate at a high angular velocity, they get into a crouched position and bring the arms in towards the body, and when they want to slow down, they get into a more upright position.  Since track and field is now in full swing, the next few posts will examine some of those events.