For example, the center of mass of a donut is in the center of its hole. Note that the center of mass does not need to be located within the object itself. The center of mass of an object of uniform density is the body’s geometric center. Similarly, the equation for linear momentum can be written in terms of the velocity of the center of mass: Note that if the net force acting on a system is zero, then the center of mass does not accelerate. Put in this form, the Second Law states that the net force acting on a system, F net, is equal to the product of the total mass of the system, M, and the acceleration of the center of mass, a cm. Our example suggests that Newton’s Second Law can be rewritten in terms of the motion of the center of mass: If we wanted to represent the diver as a point mass, this is the point we would choose. We see here that, though the diver’s head and feet and arms can rotate and move gracefully in space, the center of mass in his pelvic area follows the inevitable parabolic trajectory of a body moving under the influence of gravity. The diver’s trajectory can be broken down into the translational movement of his center of mass, and the rotation of the rest of his body about that center of mass.Ī human being’s center of mass is located somewhere around the pelvic area. That point is called the object’s or system’s center of mass.Ĭonsider the trajectory of a diver jumping into the water. We can make this simplification because there is always a point in the object or system that has the same trajectory as the object or system as a whole would have if all its mass were concentrated in that point. We can treat objects, and even systems (Say galaxies in case of inter-galactic collisions), as point masses, even if they have very strange shapes or are rotating in complex ways. This allows us to use free-body diagrams for objects with different shapes and sizes while taking into account their masses and trajectories. When calculating trajectories and collisions, it’s convenient to treat extended bodies, such as boxes and balls, as point masses.
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CENTER OF MASS FINDER HOW TO
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