The centre of mass of a rod is in the right place, halfway along it. But the centre of mass of a ring lies at the ring’s centre, that is, at a point where there is no material at all. This is an observation that helps us understand what we are doing when we introduce the centre of mass: we are not “locating the body”, we are constructing a geometric point whose trajectory obeys the same laws that governed the motion of a point particle.
The entire extended body “becomes” mathematically equivalent to a point mass: the centre of mass is the first example of that wonderful strategy in physics that consists of reducing a complicated problem to a much simpler but equivalent one (Feynman 1963; Battimelli and Stilli 1999).
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Topics: Centre of mass Concepts: Centre of mass
Related exercises: Worked exercise — The cat on the cart · Rocket that explodes mid-trajectory · Disc with a tangent hole