Kinematics
From IITJEEWiki
Kinematics deals with the study of motion without accounting or considering or trying to find the cause of motion. It is a field where we know that the body has a given rate or movement and then we use this to find the trajectory or position or time of the motion of the body!
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[edit] Rest and Motion
Imagine a moving car and that you are traveling in it. Does the driver's distance or seating change with respect to you with time? Or does the Car's speakers move when u are seeing it? The Surroundings of the car, like the trees, the road, the banner on the road side, all of these are in "motion"
Similarly, the monitor that you are viewing this on is at rest, so is your keyboard, but a bus moving on the road visible from your window is in "motion". So is a bird flying as seen from your window.
The sun, the moon, the stars and the planets change position, even when we are not moving. But then, the earth is also moving and so are the objects on the surface of the earth.
Thus, an object which appears to be at rest, may actually be in motion. (like the trees as seen from the moving car! or a platform seen from a moving train) Therefore, motion and rest are relative terms. To describe a motion, we generally use a fixed point "(called the reference point)" from which we observe if the body is moving or not. When we say that the tree is at rest it is true only in our present situation. If we were in a car, the tree might have been moving.
We cannot tell whether an object is in motion unless we have a frame of reference. The frame of reference is another object or 'point' in comparison to which an object's position changes! (Like the car in the first example!)
[edit] Types of Motion
There are 3 basic categories of motion....
- Translatory motion (Motion along a straight or curved line)
If the motion is along a straight path it is called Rectilinear Motion and if it is along a curved path it is called Curvilinear Motion
- Rotatory motion (Motion along a circular path)
- Vibratory motion (Motion which is to and fro from a fixed point)
[edit] Distance and Displacement
Think of an ant on a straight rod. It is on one end of the rod. The rod is of length 1 meter. It travels from the starting point to the end and then returns after touching the end point back to the initial point.
The distance traveled by the ant is the actual length that it traversed. This is 1+1 metres = 2 m
Distance is a scalar quantity. SI unit of distance is meter.
Now let us find out whether the position of the ant has made any change! The final position of the ant is the same as the initial position. The displacement is the "length" of the shortest path between these two points along with the direction.
Here the net displacement is zero. Because the initial and the final points are the same.
SI unit of displacement in meter. Displacement is a vector
We will consider a few more examples to discuss what the difference is between distance and displacement.
A Runner moves one full round on a circular track or radius R. The distance traveled is 2πR while the displacement is 0!
If a man goes 1 m north and then 1 meter east, His distance traveled is 2 m but the displacement of the man is √2 meters North-East
[edit] Difference in Displacement and Distance
| Displacement | Distance |
| scalar | vector |
| Equal to the length between the starting and ending point | Equal to the length traveled by the object |
[edit] Uniform Motion and Non-uniform Motion
If the body moves with constant distance, it is said to be in uniform motion. Generally refers to a straight line motion or a circular motion... It will not be generally said to refer to other shapes of trajectory.
A non uniform motion will have a change of velocity.
"Technically" a circular motion will have a changing velocity but we will often encounter phrase like "moving uniformly on a circular path" . This refers only to speed, not velociy!
