Motion along a Slanting Line

[grajee]

All,

 

I have to teach One Dimensional, Two Dimensional, and Three Dimensional Motion 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?

Thanks,
Gopi

[mathematic]

As long as the path is a straight line, it is one dimensional. The coordinate system is irrelevant.

[elfmotat]

Consider the straight line (x,y,z)=(t,t,0) where t is some parameter. (In two dimensions this is just the line y=x.) Now let's change our coordinate system by rotating it +45 degrees around the z-axis. In this coordinate system the line is given by (x,y,z)=(t,0,0). So it's just a line which is restricted to the x-axis. In general, for a line you can always rotate or translate your coordinates in such a way that the line coincides with only one axis.

[grajee]

Hello elfmotat,

 

Thank you for your clarification.

 

As per your thinking, if I change the coordinate system by rotating it 45 degree along the Z-Axis, then wouldn’t the SLANTED line in question also rotate 45 degree? In which case, the SLANTED line will be in-between the two coordinates.

Wouldn’t your interpretation work only if the SLANTED line is held in its current place so that it does not rotate along with the three coordinates by 45 degrees?

Thanks,
Gopi

[swansont]

The line doesn't rotate, only the coordinate system does.