Position
The most basic quantity in physics is position. Position tells us exactly where an object is located.
Position can be quantified as the distance and the direction of the object with respect to a chosen reference point. This reference point is the origin of a coordinate system, and position is a vector from the origin to the object.
To which part of the object ought this vector to point? This could be a complicated question, but we can simplify it by treating objects as particles: objects that have finite mass but negligible size. We shall see later that the motion of extended objects can be almost fully (with the exception of rotation) represented by the motion of a single point called the centre of mass, so this treatment is not arbitrary but is in accord with the laws of physics.
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In one dimension, position is simply a signed distance from a chosen reference point. In the figure, we set the reference point to the 7.5 cm marking of the ruler, decided a positive direction for our single coordinate \(x\): the direction of increasing numbers in the markings. This way, we can fully specify the position of any object: positive values designate positions to the right of the reference point, whilst negative values indicate that the object is to the left of the reference. |
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In two (or more) dimensions, specifying the position is more complex. After fixing the origin, we have to establish a positive direction in each dimension and specify the coordinate in that dimension the way we have seen in the one-dimensional case. In the example in the figure, we put the reference point in the lower left corner of the sheet, and choose the horizontal to the right as the positive \(x\) direction and the vertical upwards as the positive \(y\) direction. This way, the position of the ant is given by a vector drawn from the lower left corner to the middle of the ant, which is equivalent to specifying two (signed) distances: the perpendicular distance from the left edge of the sheet (the \(x\) coordinate) and the perpendicular distance from the bottom of the sheet (the \(y\) coordinate). The position vector \(\mathbf{r}\) can be given as an ordered pair of the \(x\) and \(y\) coordinates: \[\mathbf{r} = \left(x, y\right).\] In the example, the value of the position is \(\mathbf{r} = \left(4, 7.4\right)\,\mathrm{cm}.\) |
Position
The position \(\mathbf{r}\) of a particle in a given coordinate system is defined as the vector drawn from the origin of the coordinate system to the particle.
In three dimensions, the position can be quantified with the three coordinates of the particle in the given coordinate system:
\[\mathbf{r} = \left(x, y, z\right).\]
Position is a vector.
The SI unit of position is the metre.
\[\left[\mathbf{r}\right] = 1\,\mathrm{m}\]
Position is relative: in a different coordinate system, the position will be different.