All, I have to teach One Dimensional, Two Dimensional, and Three Dimensional Motions to my son and have been reading quite a bit on these topics. I still have a question and would be glad if someone can help me understand or point me in the right direction. I'm worried that I might be missing something very basic. I understand that One Dimensional motion is motion along a straight line and most of the cases, for simplicity sake, it is assumed that the motion is on the X – Axis or Y – Axis or the Z – Axis. In this case, if the motion is on the X-Axis, the Y and Z values will be 0 with X being the only Dimension. But consider the case of a motion along a straight line which is SLANTING and for simplicity sake let us assume that the slant is 45 deg. In this case, though the Z values are 0, the Y values are not, infact the (x,y) values will be (1,1)(2,2)(3,3)(4,4) … etc. So, should this motion not be classified as a Two-Dimensional motion because there are two dimensions (x,y) involved? Why is even this type of motion classified as a One-Dimensional? I understand the coordinate system can be changed by rotating it 45 degrees. But this rotation would also rotate the SLANTING line, correct? In which case, the SLANTING line will always be in between two co-ordinates. Thanks, Gopi
I don't understand that last part of your post. Nature doesn't care how we orient our coordinate axis. If you have something pointing along the North Star, and your coordinate axes are in such a way that it is in the xy plane, rotating your axes so that that direction is now along the x-axis does NOT simultaneously rotate the direction pointing to the North Star! Nature doesn't know, and doesn't care, that you just did a rotational transformation. Zz.
Suppose, if you have a SLANTING line (45 degree) in between X & Y axis and if you rotate the coordinates by 45 degrees would not (or should not) the SLANTING line also move by 45 degree? If the SLANTING line does not (or should not) move then I agree the X axis is the same as the SLANTING line.
But why would that line move? Typically, a line represented by a coordinate axis represents something physical. This could be the direction to Alpha Centuri, the direction of an inclined slope, the direction to Grandma's house... etc. It would be VERY strange if, just by rotating your graph paper, that physical direction also changes in space! Zz.
The SLANTING line also has to move since the SLANTING line is drawn with reference to X-axis and Y-axis to begin with, isn’t it? So, assuming the line is 45 degree slanting, the (x,y) values would be (1,1)(2,2)(3,3)(4,4) … etc. If the X and Y co-ordinates are rotated and if the SLANTING line is redrawn with the previous values it would still be a SLANTING line. Obviously, looks like I’m missing something. Also, could you refer me to a book that I can read and understand better? Thanks, Gopi
Hello, The line would not change its position by rotating the frame of reference. The motion is the same irrespective of the reference point one takes. For example the moon travels in the same orbit irrespective of where you see it from your location or me from another. (Considering both our frames are inertial or of the same state) Mathematics offers us the freedom to choose how to describe the motion but the physics remains same. Edit: Another example that would help in this case is a magnetic compass.....The magnetic needle would always lie in magnetic north south direction no matter how you turn, rotate , move etc. Hope this helps.
1. Take a piece of paper. 2. Draw an x-y coordinate axes any way you like. 3. Now fix that paper on your desk or on the floor so that it won't move for now. 4. Pick a particular direction to draw. This could be the direction where the window is, or a door, or a particular home decor piece. 5. Draw a straight line on your graph from the origin, along the direction of that object that you chose in #4. 6. Now rotate your graph paper by some angle. 7. While the line that you drew indicating the direction of that object you chose in #4 also rotates with your axes, it NO LONGER REPRESENTS THAT DIRECTION. The direction to that object hasn't changed! Your graph paper and the orientation of your axes have. That line pointing towards your object in #4 needs to be redrawn! 8. If you find this confusing, put a compass on the origin of your axes, and rotate your graph paper. The needle pointing north should not care that you've just rotated your axes. If it does, you may be sitting in the middle of the Bermuda Triangle. Zz.