Physics · Ch 4 — Laws of Motion
Characteristics of Centre of Mass
Characteristics of Centre of Mass
The centre of mass has a number of important general characteristics worth collecting together: (1) it is a hypothetical point at which the entire mass of a body can be assumed concentrated; (2) it is a LOCATION, not a physical quantity in itself; (3) it is the 'particle-equivalent' of an extended object, for the purpose of applying Newton's laws of motion; (4) a force applied exactly AT the centre of mass produces only linear (translational) acceleration, never any angular/rotational acceleration; (5) for a rigid body of uniform density, the c.m. coincides with the geometric centroid; (6) for a symmetric rigid body of uniform density, it coincides with the geometrical centre; (7) the location of the centre of mass can be changed ONLY by an external, unbalanced force; (8) internal forces (e.g. during a collision or an explosion) never change the location of the system's centre of mass; (9) the c.m. depends only on the distribution of mass, described via the weighted-average formula, using whatever coordinate origin is convenient; (10) for a system of particles, the c.m. need not coincide with any individual particle; (11) when balancing an object on a pivot, the line of action of its weight must pass through both the centre of mass and the pivot point (often an inherently unstable equilibrium); (12) for a system of exactly two particles, the c.m. divides the line joining them in inverse ratio of their masses, always closer to the heavier mass; (13) the c.m. is the point about which the sum of the moments of mass of the system is zero; (14) if an object has an axis of symmetry, the c.m. lies somewhere on that axis; (15) if an object has multiple axes of symmetry, the c.m. lies at their point of intersection; (16) the centre of mass NEED NOT lie within the physical body at all -- a ring or a horseshoe shape are simple examples, and (as illustrated in Picture 4.1) a high jumper performing the Fosbury Flop can have …
What this figure shows. A photograph (credited to Wikipedia) of an athlete performing a 'Fosbury Flop' high-jump technique, arching their back over a horizontal jump bar with the head and legs hanging down on either side below the bar while the torso curves above/over it. An estimated centre-of-mass/centre-of-gravity point is marked on the image, shown to lie BELOW the bar itself even though the athlete's body has cleared it -- illustrating that because the head and legs are relatively heavy compared with the thin, arched midsection passing over the bar, the body's overall centre of mass can pass UNDER the bar even while every part of the body clears it, so the increase in gravitational potential energy needed for the jump is less than if the bo …