Center of Mass
The unicycle rider carries her
partner which places the center of mass below the bottom of the wheel. Similarly ballerinas,
gymnasts, and athletes rely primarily on
controlling their centers of mass for best performances.
Master skateboarders effectively use the impulse principle to hop over obstacles while keeping their skates on their feet.
Did you know that...
Bipeds like humans cannot grow as tall as some animals like giraffes, because bipeds are intrinsically less stable than quadrupeds. Bipeds need to stabilize their centers of mass over a much smaller "footprints".
Can you balance a meter stick on a single finger? You probably know from experience that you can— if you place your finger right under the 50-cm mark. The 50-cm mark represents the special point known as the center of mass. Intuitively, the center of mass (CM) is the average location of the mass distribution of a body. For objects with a uniform mass distribution (or density), the center of mass coincides with the geometrical center. For other objects, the center of mass may not be symmetrically located. In all cases, the center of mass for any object can be located simply by the intersection of two planes (or edges) on which a rigid object can be balanced. Similarly, the CM of a freely suspended object lies on or directly below the point of suspension. When two points of suspension are used (one at a time) the intersection of the two (straight) lines of suspension locates the CM.
Q: Is the CM of a body always in physical contact with the body?
A: Not necessarily. While the CM must be confined within the smallest volume which confines the whole body, the location of the CM may actually contain no mass. The CM of a hula hoop, for example, lies in the geometrical center of the hoop, even though all the mass is distributed about the perimeter. Center of mass of a high jumper falls below him as he clears the bar.
A: You have probably correctly guessed that calculating the center of mass of an M-1 tanks with highly distributed mass and irregular shapes of various parts is very difficult. Experimentally they roll the tank over a flat platform mounted over a chassis roller. As the tank's C.M. crosses over the roller, the plate and tank will tilt. Military folks call this the Center of Balance which in reality is one of the components of the C.M. along the length of the tank.
Challenge-- Can you get up from a chair while leaning against its back? Try it. You should see that you can’t until you position your feet under the chair or lean forward.
Demo: Balance a ruler or a meter-stick horizontally on your extended forefingers. As you move your fingers closer together, they will meet right at the center of mass. The result is independent of the initial position of your fingers or even of the stick. As one finger moves, the finger closer to the CM feels the greater normal force (weight) and
consequently experiences the greater force of friction. As a result, the other finger starts to move and you can see that only one finger moves at a time.
Further Reading:
Defying Gravity (Many times athletes and dancers seem to defy gravity with their dazzling performances).