TEXAS WOMAN'S UNIVERSITY
KINS 3591
Center of Mass
INTRODUCTION
This introduction was developed by
Young-Hoo Kwon, Ph.D.,
of Texas Woman's University.
Mass is defined as 'the quantity of matter composing a body.' In every object, there is a unique point called the center of mass (CM) about which the object's mass is equally distributed. In other words, the CM is the balance point of an object.
Finding the CM of an object is an important task in biomechanics since, in many cases, the CM of an object is the point which effectively represents the whole object. Let's relate the CM with some of the issues we've been dealing with:
- Strategies to analyze the motion of an object:
General motion is mixture of both linear motion (rectilinear or curvilinear) and angular motion. We can dissect a general motion into the linear motion of the CM of the object and the angular motion of the object about its CM. In this case, CM is used as the reference point in describing the angular motion of the object.- Position, velocity & acceleration of an object:
The position, velocity and acceleration of an object is in fact identical to those of its CM, respectively. We are using the CM of the object as the representing point of the object.- Projectile motion:
We know that any object thrown into the air follows a parabolic path due to gravity. (Of course, we ignore the effects of air resistance here.) Actually, the one following a parabolic trajectory is the CM of the object, not the object itself.- Weight of an object:
Weight is the force of gravity acting between the earth and the object and is directed downward. The weight vector passes through the CM.As you see in all these examples, CM is an important biomechanical concept. It is why we need to find the CM of an object.
Finding the CM of a simple rigid object is a simple task. Since the shape of the object does not change and there is no mass shift in this kind of object, the relative location of the CM does not change. By hanging the object in different orientations, one can easily find location of the CM.
But the human body is a system of segments linked to each other at the joints. In other words, mass distribution changes continuously as the body posture changes. As a result, the relative CM location changes continuously and it is not a simple task to find the CM of the human body. The purpose of this lab is to introduce a procedure called 'the segmental method' for finding the CM of the human body.
Methods
