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Currently Playing: What happens when you choose the wrong coordinate system? #shorts #physics

What happens when you choose the wrong coordinate system? It may seem a bit strange, that a choice of coordinates makes all the difference, so let’s imagine a piece of paper and how to measure points along it. On our piece of paper, let’s say we want to locate different points. So we can give it a coordinate system, and choose an origin. Now we know choose points that have coordinates (5,0), and (-5,0). We can then use these coordinates to work out the distance between them if we wanted to. We could instead choose to impose a different coordinate system on the piece of paper - a polar coordinate system. In this system, we use coordinates called r and phi. r is the radial coordinate, meaning its value increases as we get further from the origin, regardless of what direction we go in. And phi is an angle, meaning it’s value changes as we go around the origin. Now this might seem unusual if you’ve not seen it before, but this is a perfectly valid way of representing different points on our piece of paper. In (r,phi) coordinates the SAME points from earlier now have coordinates (5,0deg), and on the other side (5,180deg). The r value is the same because they’re the same distance from the origin but the angle is different. Or we can work in radians for the angle (just another way of measuring angles, not degrees). It generally tends to work a bit better in most cases. And once again we can use the formula for working out distances between points in polar coordinates to figure out how far apart they are. We get the same distance because they’re the same points and they’re the same distance apart. Great. But the problem comes when we try to do this at the origin of this coordinate system. At this point, r = 0 - but what’s the phi value? Is it zero degrees, or 90 degrees, or 180 degrees? Well it’s all of them and none of them depending on how you want to think about it. Or in other words, this particular coordinate system works perfectly everywhere on this piece of paper EXCEPT for wherever we put the origin. #physics #understandingphysics #parthg #coordinates #polarcoordinates #cartesiancoordinates #relativity #generalrelativity #spacetime #einstein #space #cosmology #coordinatetransformation #science