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| Motion in One, Two and Three Dimensions |
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| A body is said to be in motion if its position changes with respect to its surrounding. In order to completely describe the motion of such objects, we need to specify its position. For this, we need to know the position coordinates. In some cases, three position coordinates are required, in some cases two or one coordinate is required. Based on these, motion can be classified as |
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 One dimensional motion |
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 Two dimensional motion |
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 Three dimensional motion |
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| It is also known as rectilinear or linear motion. A particle moving along a straight line is said to undergo one dimensional motion. In such a case, only one of the three rectangular coordinates changes with time. |
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| For example, if we consider one dimensional motion along the X-axis, then when the particle moves from A to B, as shown in the figure below, the X coordinate changes from x1 to x2. |
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| The straight line along which one dimensional motion takes place may be taken either along the X, Y or Z-axis. |
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| Examples of one dimensional motion are: |
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 Motion of a train along a straight line |
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 An object, like a ball, falling freely, vertically under gravity |
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 The vertical up and down oscillations of an object suspended from a vertical spring. |
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| A particle moving along a curved path in a plane has two dimensional motion. The figure below, illustrates a two dimensional motion, where a particle moves from P (x1, y1) to Q (x2, y2) along a curved path. |
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| Examples of two dimensional motion are: |
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 an insect crawling on a ball or a globe |
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 a satellite revolving round the Earth |
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 projectile motion, i.e., the two dimensional motion of a particle thrown obliquely into the air, like a baseball or a golf ball as shown below. |
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 The bob oscillates along a curved path if the simple pendulum is oscillating in a vertical plane (as shown in the figure), with a large amplitude. However, for small amplitudes, the bob approximately oscillates along a straight line, i.e., one dimensional motion. |
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| A particle moving in space has three dimensional motion. |
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| In this type of motion, all the three rectangular coordinates change with time. The figure above illustrates this type of motion where the particle moves from A to B and the corresponding rectangular coordinates change from (x1, y1, z1) to (x2, y2, z2). |
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| Examples of three dimensional motion are: |
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 A bird flying in the air |
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 A kite flying in the air |
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| Which of the graphs shown in the figure below, represents one dimensional motion of the particle? Explain why the others do not represent one dimensional motion? What is the significance of the arrows marked on some of the graphs? |
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| Solution: |
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| Graph (i) represents two different positions of the particle at the same instant of time t. This is not possible. |
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| Graph (ii) represents negative speed. This graph has no meaning since speed cannot be negative. |
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| Graph (iii) is the only graph which illustrates one dimensional motion of a particle starting from rest and moving along a straight line with increasing velocity. |
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| Graph (iv) also has no meaning since it shows velocities in opposite directions at a given time. The arrows marked in the graphs have no significance. |
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