Motion for class 7 for IIT Foundation Course

Introduction

• In everyday life, we see some objects at rest and others in motion. Birds fly, fish swim, blood flows through veins and arteries, and cars move.
• Atoms, molecules, planets, stars and galaxies are all in motion.
• We often perceive an object to be in motion when its position changes with time.
• We infer the motion of air by observing the movement of dust and the movement of leaves and branches of trees.
• What causes the phenomena of sunrise, sunset and changing of seasons? Is it due to the motion of the earth? If it is true, why don’t we directly perceive the motion of the earth?
• An object may appear to be moving for one person and stationary for some other.
• For the passengers in a moving bus, the roadside trees appear to be moving backwards.

Rest and Motion

• An object in motion is the one that changes its position with respect to it’s surroundings whereas, an object which is at rest is the one that does not change it’s position with respect to surroundings.
• The rest and motion are relative. An object at rest with respect to one observer may not be at rest with respect to another observer.
• The same can be said about motion.
• For a person inside the bus the fellow passengers are at rest but the same passengers are in motion with respect to person standing on the ground.
• If we closely observe the motion of different objects, we find them performing different kinds of motion.

Different kinds of Motions 

1. Translatory motion:-A bus moving on a road, the motion of a rising baloon, the free fall of a stone under gravity, the motion of a cricket ball when it is hit by a batsman are all examples of translatory motion.
   It is of two types rectilinear motion and curvilinear motion.
2. Rotatory motion:-In this type of motion, the object rotates about a fixed axis. The motion of blades of a ceiling fan, the spin motion of a top, the motion of turbine, the motion of earth around sun all have circulatory motion.
3. Oscillatory motion:-A boy on a swing moves to and fro. The motion such as above, where an object moves to and fro is called oscillatory motion. Pendulum of a clock, motion of a needle of a sewing machine are examples of oscillatory motion.

Distance and Displacement

Distance

Distance is defined as the length of the actual path covered by a particle in motion.
The unit of distance is centimeter in C.G.S system and meter in M.K.S or S.I. system.

Displacement

Displacement is defined as the shortest distance between the initial and final positions of a body. It is a vector quantity, whose magnitude is equal to the length of the straight line path from the initial position to the final position and the direction is along the straight line drawn from the initial to the final position.

consider a particle moving along the path ABCD as shown.

The distance travelled by the particle =6+2+5=13 m.
The displacement is the vector AD, whose magnitude is the length of the line segment AD.

Speed

• An object moving with higher speed covers a large distance in a given time or it covers a given distance in a shorter time.
• Speed is measure of fastness or the slowness of a moving object.
• It can be calculated by finding the distance covered by an object in a unit time.
• If a bus covers a distance of 40 km in one hour, then its speed is 40 km per hour.
  speed=distance/time

Kinds of speed

1. Uniform speed:-When a body covers equal distances in equal intervals of time, however small the time interval may be, then the speed of the body is said to be uniform.
2. Non-uniform speed:-When body covers unequal distances in equal intervals of time or when it covers equal distances in unequal intervals of time, then the speed of the body is said to be non-uniform. motion of bus after application of breaks is an example for non-uniform speed.

Measurement of time

• Now-a-days, clocks and watches are used for the measurement of time. They measure the time by using periodic motions. Old wall clocks use periodic motion of a simple pendulum for the measurement of time.
• A simple pendulum is made up of a metallic ball(called bob of the pendulum),suspended from a rigid support with the help of a thread. The rest position of the bob is called mean position. This type of to and fro motion is called an oscillatory motion.
• The motion of the bob of the pendulum is not only oscillatory but also periodic.
  
• The time period of a simple pendulum depends on the length of the simple pendulum and is independent of mass of the bob and its size and shape.
• The time period of a simple pendulum can be easily determined with the help of a stop watch. To find the time period, note the time taken,say for 20 oscillations and divide the time by 20.
• Now-a-days, the watches contain an electric circuit and these watches are called quartz clocks.
  Quartz clocks are more accurate than pendulum and winding clocks.

Units of Time and Speed

• The basic unit of time is second(s). The other units are minute and hour.
• Since the speed is given by distance/time, its unit is metre per second(m s^-1).
• However it can also be expressed as metre per minute(m min^-1) or kilometre per hour(km h^-1).

Distance-Time Graph

• Graphs provide a convenient method to present basic information about a variety of events.For example, in the telecast of a one-day cricket match, vertical bar graphs show the run rate of a team in each over.
• To describe the motion of an object, we can use line graphs. In this case, line graphs show dependence of one physical quantity, such as distance or velocity, on another quantity, such as time.
  
                         Distance-time graph of an object moving with uniform speed
  
• The change in the position of an object with time can be represented on the distance-time graph adopting a convenient scale of choice.
• In this graph, time is taken along the x–axis and distance is taken along the y-axis.
• Distance-time graphs can be employed under various conditions where objects move with uniform speed, non-uniform speed, remain at rest etc.
• We know that when an object travels equal distances in equal intervals of time, it moves with uniform speed.
• This shows that the distance travelled by the object is directly proportional to time taken.
• Thus, for uniform speed, a graph of distance travelled against time is a straight line.
• The portion OB of the graph shows that the distance is increasing at a uniform rate.
• you can also use the term uniform velocity in place of uniform speed if you take the magnitude of displacement equal to the distance travelled by the object along the y-axis.
  

velocity

• When an object moves with certain speed, it is not clear in which direction it is moving. To overcome the shortcoming, another term, velocity is used.
• In a way, velocity is speed in a specified direction.
• Thus, velocity consists of two parts out of which one part is direction.
• For example, a car moving with 10 m s^-1 in east direction has the magnitude of velocity as 10 m s^-1 and the direction is east.

1. Uniform velocity:- When a body moves with uniform speed in a specified direction, it is said to be moving with uniform velocity.
2. Variable velocity:- When a body moves such that either its magnitude or direction or both change, then it is said to be moving with variable velocity.
3. Average velocity:- When a body moves with variable velocity, the average velocity of the body is equal to the ratio of total displacement of the to the total time taken.
   Average velocity=Total displacement/Total time taken

Acceleration

• The change in velocity of a body per unit time is called the acceleration or the rate of change of velocity is called the acceleration.
• Example: If the velocity of the car, moving along a straight path changes from 5 m s^-1 to to 25 m s^-1 in 4 second, then its acceleration is :-Acceleration(a)=change in velocity/total time=(25-5)/4=20/4=5 ms^-1/s=5 m s^-2.
• The SI unit of acceleration is  m s^-2.
• The other units of acceleration are cm s^-2 and km h^-2.

Simple pendulum

You are already familiar with simple pendulum.Let us define few more terms associated with the simple pendulum.

• The maximum displacement of the bob of the simple pendulum, from its mean position is called amplitude.
• The length of the pendulum(l) is the distance between the point of suspension and the mid-point of the bob.
• The no.of oscillations made by the pendulum in one second is called its frequency(denoted by n).
• In SI system the unit of frequency is hertz (Hz).
• A pendulum whose time period is two seconds is called seconds pendulum.
• The time period (T) of a simple pendulum is given by: T=2π√(l/g)
  where, ‘l‘ is the length of the simple pendulum and ‘g‘ is the acceleration due to gravity.
• At a given place ‘g‘ value remains constant, T∼√l  which means time period increases with increase in length and vice-versa.