Wave motion involves the transfer of energy from one place to another without the transfer of matter. Various types of waves, such as sound waves, water waves, light waves, and electromagnetic waves, carry energy. Wave motion is responsible for transmitting heat, light, and communication signals over long distances. While the waves carry energy, the particles of the medium oscillate about a fixed location without moving along with the wave.

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Module # 05
Rest & Motion
Wave Motion
A mechanism by which energy is transferred from one place to
another is known as wave motion.
The waves carry energy, but, there is not any transfer of matter in
case of waves. When a drummer beats a drum, then, its sound is
heard at far distant points. The sound carries energy as it has the
ability to move the diaphragm of the ear. When a stone is dropped
in the still water in a pond, then, water waves move steadily along
the water until they reach the shore. If there is a small floating
object like a piece of cork in the way of these waves, then, it will
move up and down near its own location, which indicates that the
molecules of water do not move along with the wave.
Waves are responsible for the enormous amount of heat and light
received from the sun and other sources. When a bulb is turned
on, the room is flooded with light. Light waves also carry energy.
Radio and television programs are carried to us by
electromagnetic waves. It is possible to transmit an electric signal
(or a message) from one place to another due to waves.

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Although these various processes of transport of energy are
different, yet they have a common feature which we will call wave
motion.
Vibratory or Oscillatory Motion
The to and fro motion of a body about its mean position is called
vibratory or oscillatory motion. For example, when a pendulum is
disturbed from its mean position, then, it performs a vibratory
motion. Similarly, the motion of a swing falls under this category.
There is a special type of vibratory motion known as simple
harmonic motion and it plays an important role in wave motion.
Conditions for the Vibratory Motion
(1) There should be elastic restoring force.
(2) The body executing vibratory motion must possess inertia.
Translatory or Translational Motion
The motion of a body along a straight line is called translatory
motion. In this type of motion, a body moves as a whole from one
place to another. For example, the motion of a bullet fired from a
gun. That is, the motion of a body in which every particle of the
body is displaced by same amount is called translational motion

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OR
When a body is moving in a line, its motion is said to be
Translatory. The line may be straight or curved.
For example, motion of train, motion of car and motion of falling
bodies.
Keeping in view these two different definitions, it becomes
questionable whether the line must be straight or may be straight
or curved. A curve not tending to form a circle may be treated as
a line.
Rotatory or Rotational Motion
The motion of a body in a circle is called rotatory motion. For
example, the motion of a fly-wheel is rotatory motion.
Similarly, when an object spins or rotates about a fixed point or
axis, then, its motion is called rotational motion.
That is, in other words, when a body moves such that its distance
from a fixed point remains constant, then, its motion is said to be
rotatory.
For example, motion of an electric fan, rotation of the earth about
its own axis and motion of wheel of a static cycle.

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Projectile Motion
The motion of a body in a curved path, under the action of
horizontal and vertical velocities, is called projectile motion. The
body itself is called the projectile while the path of the projectile is
called trajectory.
Examples of projectile:
(1) A bullet shot from a gun
(2) An object falling from an aeroplane
(3) A cricket ball hit into air.
Positive Acceleration
If speed is increasing, then acceleration is positive and its
direction is in the direction of motion.
Periodic Motion or Harmonic Motion
Any motion that repeats itself in equal intervals of time is called
periodic motion or harmonic motion.
Periodic Time
The time taken for a wave particle to make one complete
oscillation is called the periodic time.

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Oscillatory or Vibratory Motion
If a particle moves back and forth over the same path, we call the
motion as oscillatory or vibratory.
The common examples are:
(1) The swinging bob of a pendulum,
(2) Balance wheel of a watch,
(3) A violin string,
(4) A mass attached to a spring, and
(5) Oscillating air molecules carrying sound waves
produced by the violin or a tuning fork.
Wave Motion
A mechanism by which energy is transferred from one place to
another is known as wave motion.
The waves carry energy, but, there is not any transfer of matter in
case of waves. When a drummer beats a drum, then, its sound is
heard at far distant points. The sound carries energy as it has the
ability to move the diaphragm of the ear. When a stone is dropped
in the still water in a pond, then, water waves move steadily along
the water until they reach the shore. If there is a small floating
object like a piece of cork in the way of these waves, then, it will

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move up and down near its own location, which indicates that the
molecules of water do not move along with the wave.
Waves are responsible for the enormous amount of heat and light
received from the sun and other sources. When a bulb is turned
on, the room is flooded with light. Light waves also carry energy.
Radio and television programs are carried to us by
electromagnetic waves. It is possible to transmit an electric signal
(or a message) from one place to another due to waves.
Although these various processes of transport of energy are
different, yet they have a common feature which we will call wave
motion.
Vibratory or Oscillatory Motion
The to and fro motion of a body about its mean position is called
vibratory or oscillatory motion. For example, when a pendulum is
disturbed from its mean position, then, it performs a vibratory
motion. Similarly, the motion of a swing falls under this category.
There is a special type of vibratory motion known as simple
harmonic motion and it plays an important role in wave motion.
Conditions for the Vibratory Motion
(1) There should be elastic restoring force.

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(2) The body executing vibratory motion must possess inertia.
Uniform Circular Motion
If a body moves in a circular path and moves with a uniform
(constant) speed, it is said to be in a uniform circular motion.
Let us consider the motion of an object which moves along the
circumference of a circle with constant speed.
Figure shows that the direction of motion at any point is given by
the tangent at that point. Tangents have been drawn at points x, y
and z which show the direction of motion of the object at these
points.
Directions of the tangents show that the direction of motion of the
object is constantly changing. We know that an object possesses
uniform velocity only when both its speed and direction remain
unchanged. Since the direction of motion of the above mentioned
object is changing at every instant, therefore, its velocity is also
changing at every instant.
Fig :( 1) Uniform circular motion

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This shows that there is an acceleration in the motion of the
object. If the acceleration is in the direction of the force then the
magnitude of the velocity, i.e., the speed will increase and the
direction of velocity will remain constant.
However, if the direction of acceleration is perpendicular
to the direction of motion then the magnitude of velocity will
remain the same but its direction will change. In the present case
the object moves with uniform speed only.
Therefore, the direction of acceleration is perpendicular to the
direction of motion. In figure, if we draw perpendiculars at points
x, y and Z, then the direction of acceleration would be towards the
centre of the circle. It is, therefore, called centripetal acceleration.
It can be shown that the magnitude of centripetal acceleration is
directly proportional to the square of the speed and inversely
proportional to the radius of the circle. Mathematically, for an
object of mass m, moving with a speed v on a circular path of
radius r, the magnitude of the centripetal acceleration ac is given by
ac  v2
&
ac  1/r
By combining these two, we get,

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ac  v2
/r
OR
ac = k v2
/r
Where k is a constant and its value is 1. Therefore,
ac = v2
/r
Translatory or Translational Motion
The motion of a body along a straight line is called translatory
motion. In this type of motion, a body moves as a whole from one
place to another. For example, the motion of a bullet fired from a
gun. That is, the motion of a body in which every particle of the
body is displaced by same amount is called translational motion
OR
When a body is moving in a line, its motion is said to be
Translatory. The line may be straight or curved.
For example, motion of train, motion of car and motion of falling
bodies.
Keeping in view these two different definitions, it becomes
questionable whether the line must be straight or may be straight
or curved. A curve not tending to form a circle may be treated as
a line.

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Rest
When a body does not change its position with respect to its
surroundings, then, the body is said to be in state of rest.
Thus, a body is said to be at rest if its position relative to its
surroundings does not appear to change, e.g. a train is
considered to be at rest on the platform by a person sitting on the
platform if the train does not move and does not change its
position relative to the platform.
Rotatory or Rotational Motion
The motion of a body in a circle is called rotatory motion. For
example, the motion of a fly-wheel is rotatory motion.
Similarly, when an object spins or rotates about a fixed point or
axis, then, its motion is called rotational motion.
That is, in other words, when a body moves such that its distance
from a fixed point remains constant, then, its motion is said to be
rotatory.
For example, motion of an electric fan, rotation of the earth about
its own axis and motion of wheel of a static cycle.
Projectile Motion
The motion of a body in a curved path, under the action of

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horizontal and vertical velocities, is called projectile motion. The
body itself is called the projectile while the path of the projectile is
called trajectory.
Examples of projectile:
(1) A bullet shot from a gun
(2) An object falling from an aeroplane
(3) A cricket ball hit into air.
Motion
A body is said to be in a state of motion if its position continuously
changes with respect to its surroundings. For example, a cyclist
feels his motion only by looking at the objects around him which
seem to move away (or back).
If a body A is changing its position with respect to another body B,
then, body A is in motion with respect to body B. When bodies A
and B are not changing their positions with respect to each other,
then, they may be in motion with respect to another body C. For
example, passengers are at rest with respect to the walls of a
moving train cabin, but, they are in motion with respect to the
passengers at platform. Therefore, rest and motion are relative
terms.

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Types of Motion
There are three types of motion.
1 Translatory motion
2 Rotatory motion
3 Vibratory motion
Circular Motion
The universe is full of a large number of objects which move in
nearly circular paths. When an object moves with uniform speed
in a circular orbit, its acceleration must be directed towards the
centre, otherwise, it will have component along the direction of the
motion which will change its speed.
The acceleration which makes the object to move in a circular
orbit is provided by some force. In the case of planets, it is the
gravitational force which provides the necessary acceleration. For
a moving car clearing a curve on a perfectly level road, it is
provided by the force of friction between the road and the tyres.
The coulomb force of attraction between the nucleus and the
electron is responsible for the nearly circular motion of the
electron around the nucleus.

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Motion under Gravity
Following are the important points for the bodies falling under
gravity.
1 Bodies falling freely have initial velocity equal to Zero and
their acceleration is positive.
2 All objects thrown vertically upward have negative
acceleration equal to
- 9.8 ms-2
and at the highest point their final velocity becomes
Zero.
3 When an object is thrown vertically upward, then, at the
highest point its final velocity becomes Zero. But, when, this
object returns to the earth, then, this final velocity becomes equal
to the initial Velocity. Thus its initial velocity will be Zero.