CHAPTER 8

MOTION

INTRODUCTION• We use the word Rest very often. For

example, when someone is doing no work or lying on the bed, we often say that the person is resting. This mean the person is not moving. Scientifically as well, the word Rest has a similar meaning.

• Scientifically we say an object is at rest when the position of the object does not change with time with respect to its surroundings.

• Similarly, motion is defined as the change of position of an object with time, with respect to its surroundings.

WHAT DO YOU MEAN BY WITH RESPECT TO ITS

SURROUNDINGS?• We know that moving train Is

motion because its position changes with time. Now consider a person sitting in the train for someone standing on the platform the person sitting in the train is motion. But for the co-passengers, the person at rest as the position of the person does not change with time. Therefore, we need to consider the surroundings or the point of observation while describing the state of motion of an object. The surroundings called reference frame.

TYPES OF MOTION

Motion can be broadly classified into three main categories:-

1} Translatory motion 2} Rotational motion 3} Periodic motion

TRANSLATORY MOTION

• Translatory motion is the motion of a particle in a straight line. A bus travelling in a straight road and an apple falling from a tree are the examples of this kind of motion.

ROTATIONAL MOTION

• Rotational motion refers to the motion of a body around a fixed axis. A spinning top, a bead moving on a circular track and earth’s rotation are example of this kind of motion.

Periodic motion• Periodic motion reference to the

motion that is repeated in a regular interval of time. An oscillation spring and the motion of planet around the sun illustrate are example of type of motion.

LINEAR MOTION • The word Linear means Straight and

the word motion means Change in position with respect to a frame of reference. So, a body moving in a straight line with respect to a frame of reference is said to be a linear motion. An example of this is the motion of an ant on a straight wire.

• Points to remember regarding linear motion:-

• In linear motion, the object must move in a straight line

• The motion of the object among the straight line may not be uniform

UNIFORM MOTION

• If a body covers equal distances along a straight line in regular intervals of time, then the motion is said to be uniform for example:- a ball pushed in a free space will continue to move uniformly, covering equal distance in equal intervals of time along a straight path. If an art covers equal distance in equal intervals time along a straight wire, its is motion is uniform.

NON-UNIFORM MOTION

• If a body covers unequal distance in a regular intervals of time, then the motion said to be non-uniform motion

for example:- The ball take a curved path when thrown. Its direction of motion changes with time. Also, its covers unequal distances in regular of time. So, its motion is non-uniform.

PHYSICAL QUANTITY• A physical quantity is a type of

physical property that can be expressed in a number. For example, time is a physical quantity as it can be expressed in number, but anger is not as it is cannot be expressed in numbers.

• Physical quantity can be classified into two types:-

• Scalar quantities • Vector quantities

SCALAR QUANTITIES • If a physical quantity can be

completely described only by its magnitude, then it is a scalar quantity. To measure the mass of an object, we only have to know how much matter is present in the object. Therefore, mass of an object is a physical quantity that only requires magnitude to be expressed. Therefore, we say that mass is a scalar quantities.

• some more examples of scalar quantities are time, area, volume and energy.

VECTOR QUANTITIES • There are some physical quantities

that cannot be complete described on by their magnitudes. These physical quantities require direction along with magnitude. For examples, if a consider force, then along with the magnitude of the force, we also have to know the direction along which the force is applied. Therefore, to describe a force, we require both its magnitude and direction. This type of physical quantity is called vector quantity.

DISTANCE• Distance is the length of the path or

the path length travelled by a body while moving from a initial position to a final position.

• It is a scalar quantities its SI unit is meter (m).therefore only magnitude is important not the direction of movement (implies that path can never be negative).

DISPLACEMENT• Displacement is the shortest

distance between the initial and final position of the body. It is a vector quantities it SI unit is also meter (m).

• In displacement, the direction of motion is always directed from the initial position towards the final position.

SPEED• Speed is defriend as the rate of

distance covered body. • Mathematically, speed is given speed= distance travelled time taken It is a scalar quantity; that means no direction is required impues that speed cannot be negative.

AVERAGE SPEED • A body travelling from one location

to another might stop, slow down, speed up or move at constant speed.

• The average speed of body is defined as the distance travelled divided by a total time taken

• Mathematically, average speed is given as = total time

distance

VELOCITY• When we include the direction of

motion with speed, we are talking of physical quantity called velocity. Thus, velocity is speed with direction. Velocity is defined as the rate of change of displacement. velocity = displacement

time interval It is vector quantity. Therefore, direction of movement is important.(implies that velocity contains algebraic sign)

AVERAGE VELOCITY• A body moving from one point to

another may change its velocity a number of times, but it will have an average velocity its journey. Average velocity of a body is defined as the net displacement divided by the total time of travel.it is a vector quantity. Its SI is meter per second (m/s) and it can be positive, negative or zero,average velocity= initial+final velocity

period of time

ACCELERATION • Acceleration is defined as the rate of

change of velocity. It is a vector quantity and its direction is given by the direction of the force casing the acceleration. Mathematically, acceleration Is given as:- acceleration= change in velocity Time taken suppose the velocity of a car is u at time t, later at time t2 its velocity become v change in velocity = (v-u)time interval

UNIFORM ACCELERATION• If the rate of change of velocity

remains constant, then the acceleration is uniform . Example of uniform acceleration include a ball under free fall a boll rolling on an inclined plane and a car accelerating on a straight, traffic free road.

NON-UNIFORM ACCELERATION

• If the rate of change of velocity changes with time, then the acceleration is non-uniform . An example of non-uniform acceleration is a car accelerating on a straight road with a traffic.

GRAPHICAL REPRESENTATION OF MOTION :-a) Distance – Time graphs :- The change in the position of a body with time can be represented on the distance time graph. In this graph distance is taken on the y – axis and time is taken on the x – axis.

A

B

10

20

30

t1 t2

s1

s2

C

Time (s)

Dis

tan

ce (

m)

X

Y

5 10 15 20

Distance – time graph for a body moving with uniform speed

0

ii) The distance – time graph for non uniform motion is non linear. This is because in non uniform speed a body travels unequal distances in equal intervals of time.20

40

Time (s)

Dis

tan

ce (

m)

X

10

30

50 10 15 20

Distance – time graph for a body moving with non uniform speed

Y

B) VELOCITY – TIME GRAPHS :-

The change in the velocity of a body with time can be represented on the velocity time graph. In this graph velocity is taken on the y – axis and time is taken on the x – axis.

20

40

Time (s)

Vel

oci

ty (

km h

-1)

X

10

30

50 10 15 20t1 t2

A B

C D

Velocity – time graph for a body moving with uniform velocity

Y

ii) If a body whose velocity is increasing with time, the graph is a straight line having an increasing slope. This is because the velocity increases by equal amounts with equal intervals of time.

A

B

10

20

30

t1 t2 C

Time (s)

Vel

oci

ty (

m s

-1)

X

Y

10 20 30 40

Velocity – time graph for a body moving with uniform acceleration

D

E

0

iii) If a body whose velocity is decreasing with time, the graph is a straight line having an decreasing slope. iv) If a body whose velocity is non uniform, the graph shows different variations.

20

40

Time (s)

Vel

oci

ty (

ms-1

)

X

10

30

50 10 15 20

20

40

Time (s)

Vel

oci

ty (

ms-1

)

X

10

30

50 10 15 20

Velocity – time graph for a uniformly decelerated motion

Velocity – time graph for non uniform acceleration

Y Y

6) EQUATIONS OF MOTIONS BY GRAPHICAL METHOD :-

The motion of a body moving with uniform acceleration can be described with the help of three equations called equations of motion. The equations of motion are :- i) v = u + at ii) s = ut + ½ at2

iii) 2as = v2 – u2

A) EQUATION FOR VELOCITY Consider a velocity – time graph for a body moving with uniform acceleration ‘a’. The initial velocity is u at A and final velocity is v at B in time t.

Time (s)

Vel

oci

ty (

ms-1

)

XO

Velocity – time graph for a uniformly accelerated motion

Y

t

u

v

A

B

C

D

E

B) EQUATION FOR POSITION

Consider a velocity – time graph for a body moving with uniform acceleration ‘a’ travelled a distance s in time t.

Time (s)

Vel

oci

ty (

ms-1

)

O

Velocity – time graph for a uniformly accelerated motion

t

u

v

A

B

C

D

E

C) EQUATION FOR POSITION Consider a velocity – time graph for a body moving with uniform acceleration ‘a’ travelled a distance s in time t. The distance travelled by the body between the points A and B is the area OABC. s = area of trapezium OABC

Time (s)

Vel

oci

ty (

ms-1

)

O

Velocity – time graph for a uniformly accelerated motion

t

u

v

A

B

C

D

E

7) CIRCULAR MOTION :- The motion of a body in a circular path is called circular motion. v= 2лr t