If the objects do not conveniently lie along a line, you can calculate the x and y
positions of the center of mass by applying the equation in each dimension separately.
The result is the x,y position of the system’s center of mass.
xCM = x position of center of mass
mi = mass of object i
xi = x position of object i
What is the location of the center
of mass?
xCM = 32/5.0
xCM = 6.4 m
7.15 - Center of mass and motion
Above, you see a ballet dancer performing a grand jeté, a “great leap.” When a ballet dancer performs this leap well, she seems to float
through the air. In fact, if you track the dancer’s motion by noting the successive positions of her head, you can see that its path is nearly
horizontal. She seems to be defying the law of gravity. This seeming physics impossibility is explained by considering the dancer’s center of
mass. An object (or a system of objects) can be analyzed by considering the motion of its center of mass.
Look carefully at the locations of the dancer’s center of mass in the diagram. The center of mass follows the parabolic path of projectile motion.
To achieve the illusion of floating í moving horizontally í the dancer alters the location of her center of mass relative to her body as she
performs the jump. As she reaches the peak of her leap, she raises her legs, which places her center of mass nearer to her head. This
Center of mass and motion
Laws of mechanics apply to center of
mass
Shifting center of mass creates "floating"
illusion