# Motion / Moving Objects

### Introduction

We see so many moving objects everyday like moving buses, trains, running cricketers, flying aeroplanes, moving ships etc. When we are sitting in a moving train, the things outside appears to be moving. When the train stops at platform, the things outside move when they are in motion. But if the another train is passing our train which is stationary on the platform, our train appears to be moving.

The motion is the movement of a body. The motion is with respect to another object which is assumed to be stationary. **
**“A body is said to be in motion when its position changes continuously with respect to a stationary object. Here the stationary object is taken as reference point.Therefore, the motion is a relative concept . The reference point chosen decides whether the object is stationary or moving.”

An object may appear to be moving for one person and it may appear stationary for some other person. One such example is a person A, sitting in the moving bus. The person A appears moving to the person B, standing on the bus-stand. However, the person A appears to be stationary to the another person C, who is sitting with him in the moving bus.

### Types of motion

**Rectilinear motion**– Some objects move in a straight line. For example,

(i) a ball rolling on a horizontal surface,

(ii) a ball falling from a building .

In the both examples, objects change their positions with time along a straight line. This type of motion is called rectilinear motion.**Circular motion**– Observe the motion of a second’s hand of a clock, or motion of a child sitting on a marry-go round, or the motion of the blades of an electric fan. In such a motion, an object follows a circular path during motion. This type of motion is called circular motion. If you take a stone, tie a thread to it and whirl it with your hand, you will find that the stone moves on a circular path. In all such cases, though an object changes its position with time, it remains at a fixed distance from a point.**Oscillatory motion**– Some objects move to and fro, such as a swing, a pendulum, the branches of a tree in the wind and the needle of a sewing machine. Such type of motion is called oscillatory motion. In such a motion, an object oscillates about a point, often called.*equilibrium position*

### Scalar and Vector quantity

All the quantities are of two types either scalar or vector.

**Scalar quantity**– It has magnitude but no direction such as length, mass, time.

For examples -A ball of 45 g has mass, but no direction, it means, it is a scalar quantity.**Vector quantity**– Some quantities have magnitude as well as direction which are called vector quantities. Force has magnitude and direction, like 5N force in upward direction or in downward direction. The direction of force makes difference. Displacement, velocity and acceleration are all vector quantities.

Scalar quantities are added like ordinary numbers. But vector quantities are added with different rules. The vectors in same direction can be added easily.

For example sum of vector A and vector C is vector D which is obtained by adding the magnitudes of A and C because A and C have same direction. This is shown in fig.1.

Fig.2 shows the subtraction of vectors A and C . The magnitude of resultant vector E is obtained by subtracting magnitude of C from A .

### Distance and displacement

**Motion along a straight line** –

- An object starts from point O and travel towards east . This is shown in fig.3. The object reaches to point A. The distance traveled by the object is 40m. The displacement of the object is OA towards east which is 40 m. Now the object moves towards west and reaches to point B.The distance travelled by the object =

OA + AB = 40 + 25 = 65 m.The displacement of the object is OB. It is equal to = 40 – 25 = 15m towards east.That means, in this motion, the magnitude of displacement (25m) is less than the distance travelled (55m).

*Therefore, magnitude of displacement is either equal or less than the magnitude of distance.* - Observe fig. 4 .

A person moves from A to B and then B to C .The distance travelled by the person is AB + BC = 5 + 3 = 8 km.However, the distance from A to C is 4 Km, therefore the person has moved 4 km along AC.The distance is a scalar quantity. Therefore, it has been added like ordinary numbers but displacement is a vector quantity and displacement along AC is 4 km which is the component of AB along AC. - Thus,

(a)* When a body moves from one point to another, the distance traveled refers to the actual length of the indirect path (in above case AB + BC) whereas displacement refers to the straight line path between the initial and the final positions (in above case A and C).*

(b) **The distance traveled by a moving body cannot be zero but the final displacement of a moving body can be zero.** For example in fig.4 the person moves from A to B, B to C and C to A then the distance is AB + BC + CA = 5 + 3 + 4 = 12 km as it is a scalar quantity.

The displacement is zero because the moving body finally comes back to its starting point.

Similarly, if we travel along a circular track of radius ‘r’ and reach back at the starting point A, then though the distance traveled is 2πr but our final displacement will be zero.