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# An introduction to Motion, Point object & Coordinates of origin

The branch of physics which deals with the action of forces on objects are called mechanics. The branches of mechanics are statics,  dynamics and kinematics. Statics deals with the forces acting on objects at rest or in equilibrium. Kinematics deals with the motion of objects without considering the causes of motion. Dynamics deals with the motion of objects by considering the causes of motion.

## What is the difference between rest and motion?

• A body is said to be in a state of rest if it does not change its position with respect to its surroundings.
eg: Chair, Building etc
• A body is said to be in motion if it continuously changes its position with respect to any fixed point.
eg: A moving bus, the motion of the moon around the earth, etc.

Some examples for motions invisible to us are the motion of gas molecules, the motion of the galaxy, the motion of the electrons in atom etc.

Rest and motion are relative terms. For example, a building is at rest for an observer on the earth, while it is in motion when observed from outer space.

## What is the difference between one dimensional, two dimensional and three-dimensional motion?

• If a body moves in a straight line path, its motion is considered as one-dimensional motion.
Eg: An ant moving on a stretched wire, a train running on straight rails, a car moving along a straight road etc.
• If a body is free to move in any direction in a plane surface, then its motion is said to be a two-dimensional motion.
Eg: The movement of a carrom coin, an ant moving on a table, a ball rolling over the ground, the movement of the tip of a pen while writing etc.
• If a body is free to move in any direction in space, then its motion is said to be three-dimensional.
Eg: A fish moving under water, the motion of a bird, the motion of an aeroplane, the motion of a kite etc.

## Point Object

An object is said to be a point object if its dimensions(length, breadth, thickness etc.) are negligible in comparison with the distance covered by it. i.e., a point object is an object whose size is negligible and hence it can be represented by a point. However, the mass of the point object is the same as the mass of the object under consideration. In dynamics, a point object is usually referred to as a particle.

Example:

1. The length of a bus may be neglected compared with the length of the road it is running.
2. In describing planetary motions, the size of the planet is ignored compared with the size of the orbit in which it is moving.
3. Similarly, a molecule in a large container, an aeroplane or a train covering a large distance etc can also be treated as point objects.

## Coordinates of origin in a graph

For various physical events, we have to assign different times of occurrence. For this, some instant of time is chosen as the origin of time. At the origin, time is taken to be zero. Time is represented in a convenient unit. The events which occur after the origin of time will be assigned a positive number of time units while the events which took place before the origin will carry a negative number of time units.

For example, consider a train which starts from station A at 2 a.m. and passes station B at 5 a.m., C at 10 a.m., and D at 4 p.m. Choosing 5 a.m. as the origin of time, the information is given in the below figure 1.

So we can define origin as the point of intersection of all the axes of a coordinate system and is usually labelled with the letter O. All the coordinates are zero at the point of origin. In a two-dimensional coordinate system, the origin is the point where the x-axis and y-axis intersect and it has the coordinates (0,0). Similarly, in a three-dimensional coordinate system, the origin is the point where the x-axis, y-axis and z-axis intersect and is having the coordinates (0,0,0).

## Solved Problems

1. Find out the new coordinates of the point  (8,5) if the origin is shifted to the point (3,1) by the translation of axes.

Ans:

Let, the new origin be (p, q) = (3,1) and the given point be (x,y) = (8,5)
Let the new co-ordinates be (X,Y)
Therefore, x = X + p and y = Y + q
Substituting, we get, 8 = X + 3 and 5 = Y + 1
⇒  X = 8 – 3 and Y = 5 – 1
i.e., we get, X = 5 and Y = 4
Thus the new coordinates are (5, 4)

2. Draw the graph of the equation x = 3

Ans:

To draw the graph of the equation x = 3, plot the intercept on the x-axis and draw a vertical line through that point.

That is, the graph of x = 3 is a vertical line passing through the point (3, 0), the x-intercept. At every point of that line, the x-coordinate is always 3.

3. Plot the graph of the equation y = 2

Ans:

To draw the graph of the equation y = 2, plot the intercept on the y-axis and draw a horizontal line through that point.

That is, the graph of y = 2 is a horizontal line passing through the point (0, 2), the y-intercept.  At every point of that line, the y-coordinate is always 2.

4. Draw the graph of the equation x = -4

Ans:

To draw the graph of the equation x = -4, plot the intercept on the x-axis and draw a vertical line through that point.

That is, the graph of x = -4 is a vertical line passing through the point (-4, 0), the x-intercept.  At every point of that line, the x-coordinate is always -4.

5. Plot the graph of the equation 4x – 6y = 12

Ans:

To plot the equation, first find out the x-intercept and y-intercept.
The given equation is 4x – 6y = 12
In order to find the x-intercept, assume y = 0 and solve the equation for x.
i.e., y = 0,
⇒  4x – 6 × 0 = 12
⇒  4x = 12
∴    x = 12/4 = 3
i.e., the x-intercept is (3, 0).

Similarly, In order to find the y-intercept, assume x = 0 and solve the equation for y.
i.e., x = 0,
⇒  4 × 0 – 6y = 12
⇒  -6y = 12
∴   y = -(12/6) = -2
i.e., the y-intercept is (0, -2).

Now plot the x-intercept and y-intercept on a graph and join the points through a straight line.

6. Draw the graph of the equation 3x + 11 = 5

Ans:

To plot the equation, first solve the equation to find out the intercepts.
The given equation is 3x + 11 = 5
First, solve the equation for x to find the x-intercept.
i.e., 3x + 11 = 5
⇒   3x = 5 – 11
⇒   3x = -6
⇒    x = -6 / 3 = -2
That is, the x-intercept is (−2, 0). Now mark the point on the graph and draw a vertical line through that point.

7. Plot the graph of the equation 4y – 12 = 0

Ans:

To plot the equation, first find out the x-intercept and y-intercept. Here, there is no x-intercept and solve the equation to find out the y-intercept
The given equation is 4y – 12 = 0
First, solve the equation for y to find the y-intercept.
i.e., 4y – 12 = 0
⇒   4y = 12
⇒    y = 12 / 4 = 3
That is, the y-intercept is (0, 3). Now plot the intercept on the y-axis and draw a horizontal line through that point.