How can we measure the position of an object if every point in it has a different position? For example if we want to measure the position of a human body, how can we do that when his arms and legs and all points within his body have different positions?
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2 Answers
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Distance is defined between between 2 points. Hence when someone says an object is at a certain distance from the reference, they generally refer to the distance between centre of mass of the object and the reference.
answered Mar 26, 2021 at 9:52
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Use the centre-of-mass.
Imagine throwing, say, an axe at an axe-throwing competition. The axe spins around itself while flying forwards. That means, it does have a flying path as a whole because the axe is obviously moving forwards, but each point on the hammer superimposes a path on top of this main flying path. A point on the shaft moves very differently from a point at the edge.
But there is actually one point which does not superimpose any fluctuations from the main path. One single point that flies through the air in a smooth parabola, just as we would predict a point mass to do. That point is called the centre-of-mass.
The centre-of-mass is the point on any object about which all rotational tendencies "cancel out".* Meaning, if you look at an edge-point on the axe, while in natural rotation that point is sometimes below and sometimes above the point that is a centre-of-mass. The positions of this edge-point will together "cancel themselves out" when added up with signs. The centre-of-mass is the point about which all other points are spinning, while this point itself is not spinning.
If you want to pick a point to represent your object, then pick this one. When you want to refer to an object's position or speed etc., then we all unconsciously understand that you are referring to the position and speed of the centre-of-mass.
* The centre-of-mass is also the balance point about which gravity cancels out. So to find the centre-of-mass, just hang the object in a string from any point, and the centre-of-mass will align itself just below it. Then hang the object from some other point, and the centre-of-mass will again align itself below it. Then from such two freely hanging tests, you'll know where the centre-of-mass is. (Gravity actually cancels out around the centre-of-gravity*, but the centre-of-gravity and centre-of-mass coincide when gravity is the same all through the body, which is the case for human-scale objects.)*