- Definition 1: Position
- The position of a particle is a point in the defined volumetric space of the coordinate system.
Position of a point object |
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The position of a point like object, in three dimensional coordinate space, is defined by three values of coordinates i.e. x, y and z in Cartesian coordinate system as shown in the figure above.
It is evident that the relative position of a point with respect to a fixed point such as the origin of the system “O” has directional property. The position of the object, for example, can lie either to the left or to the right of the origin or at a certain angle from the positive x - direction. As such the position of an object is associated with directional attribute with respect to a frame of reference (coordinate system).
Example 1: Coordinates
Problem : The length of the second’s hand of a round wall clock is ‘r’ meters. Specify the coordinates of the tip of the second’s hand corresponding to the markings 3,6,9 and 12 (Consider the center of the clock as the origin of the coordinate system.).
Coordinates of the tip of the second’s hand |
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Solution : The coordinates of the tip of the second’s hand is given by the coordinates :
3 : r, 0, 0
6 : 0, -r, 0
9 : -r, 0, 0
12 : 0, r, 0
Exercise 1
What would be the coordinates of the markings 3,6,9 and 12 in the earlier example, if the origin coincides with the marking 6 on the clock ?
Coordinates of the tip of the second’s hand |
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Solution
The coordinates of the tip of the second’s hand is given by the coordinates :
3 : r, r, 0
6 : 0, 0, 0
9 : -r, r, 0
12 : 0, 2r, 0
The above exercises point to an interesting feature of the frame of reference: that the specification of position of the object (values of coordinates) depends on the choice of origin of the given frame of reference. We have already seen that description of motion depends on the state of observer i.e. the attached system of reference. This additional dependence on the choice of origin of the reference would have further complicated the issue, but for the linear distance between any two points in a given system of reference, is found to be independent of the choice of the origin. For example, the linear distance between the markings 6 and 12 is ‘2r’, irrespective of the choice of the origin.