CHAPTER –4
-: LAWS OF MOTION:-
Point mass: - An object can be considered as a point object if during motion in a given time, it
covers distance much greater than its own size.
Object with zero dimension considered as a point mass.
Point mass is a mathematical concept to simplify the problems.
Force:-
Force is an external effect in the form of a push or pulls which,
(i) Produces or tries to produce motion in a body at rest.
(ii) Stops or tries to stop a moving body.
(iii) Changes or tries to change the direction of motion of the body.
Dimension: Force = mass × acceleration. F = [MLT-2].
Absolute units (i) Newton (S.I. (ii) Dyne (C.G.S)
Gravitational units: (i) Kilogram-force (M.K.S.) (ii) Gram-force (C.G.S).
One Newton is that force which produces an acceleration of 1m/s2 in a body of mass 1
Kilogram. 1N =1kgm/s2.
1 Dyne: One dyne is that force which produces an acceleration of 1cm/s2 in a body of
mass 1g. 1D = 1gcm/s2.
1N = 105 D.
1kgf = 9.8 N.
Out of so many natural forces, for distance 1015 m., nuclear force are strongest while
gravitational force weakest.
F nuclear > Electromagnetic > F gravitational .
INERTIA-
Inherent property of all the bodies by virtue of which they cannot change their state of rest or
uniform motion along a straight line by their own is called inertia.
Inertia is not a physical quantity; it is only a property of the body which depends on
mass of the body.
Inertia has no units and no dimensions
Two bodies of equal mass, one in motion and another is at rest, possess same inertia
because it is a factor of mass only and does not depend upon the velocity.
Inertia means ‘resistance to change’. A body does not change its state of rest or uniform
motion, unless an external force compels it to change that state.
Umakanta Sir’s class note Page 1
,Types of inertia:-
(a) Inertia of rest: - It is the inability of a body to change by itself, its state of rest. This
means a body at rest remains at rest and cannot start moving by its own.
Example:
A person who is standing freely in bus, thrown backward, when bus starts suddenly.
When a bus suddenly starts, the force responsible for bringing bus in motion is also
transmitted to lower part of body, so this part of the body comes in motion along with
the bus. While the upper half of body (say above the waist) receives no force to
overcome inertia of rest and so it stays in its original position. Thus there is a relative
displacement between the two parts of the body and it appears as if the upper part of
the body has been thrown backward.
Note: - If the motion of the bus is slow, the inertia of motion will be transmitted to the
body of the person uniformly and so the entire body of the person will come in motion
with the bus and the person will not experience any jerk.
When a horse starts suddenly, the rider tends to fall backward on account of inertia of
rest of upper part of the body as explained above.
A bullet fired on a window pane makes a clean hole through it while a stone breaks the
whole window because the bullet has a speed much greater than the stone. So its time
of contact with glass is small. So in case of bullet the motion is transmitted only to a
small portion of the glass in that small time. Hence a clear hole is created in the glass
window, while in case of ball, the time and the area of contact is large. During this time
the motion is transmitted to the entire window, thus creating the cracks in the entire
window.
If we place a coin on smooth piece of card board covering a glass and strike the card
board piece suddenly with a finger. The cardboard slips away and the coin falls into the
glass due to inertia of rest.
The dust particles in a blanket fall down when it is beaten with a stick. This is because
the beating sets the blanket in motion whereas the dust particles tend to remain at rest
and hence separate.
(b) Inertia of motion :
It is the inability of a body to change itself its state of uniform motion i.e., a body in
uniform motion can neither accelerate nor retard by its own.
Example:
When a bus or train stops suddenly, a passenger sitting inside tends to fall forward. This
is because the lower part of his body comes to rest with the bus or train but the upper
part tends to continue its motion due to inertia of motion.
Umakanta Sir’s class note Page 2
, An athlete runs a certain distance before taking a long jump. This is because velocity
acquired by running is added to velocity of the athlete at the time of jump. Hence he
can jump over a longer distance
A person jumping out of a moving train may fall forward.
(c) Inertia of direction:-
It is the inability of a body to change by itself direction of motion.
Example:-
When a stone tied to one end of a string is whirled and the string breaks suddenly, the
stone flies off along the tangent to the circle. This is because the pull in the string was
forcing the stone to move in a circle. As soon as the string breaks, the pull vanishes. The
stone in a bid to move along the straight line flies off tangentially.
The rotating wheel of any vehicle throw out mud, if any, tangentially, due to directional
inertia.
When a car goes round a curve suddenly, the person sitting inside is thrown outwards.
Common forces in mechanics:-
(i) Weight: Weight of an object is the force with which earth attracts it. It is also called
the force of gravity or the gravitational force.
(ii) Normal force: When a body is placed on a rigid surface, the body experiences a force
which is perpendicular to the surfaces in contact. Then force is called ‘Normal force’
or ‘Reaction’.
(iii) Tension: The force exerted by the end of taut string, rope or chain against pulling
(applied) force is called the tension. The direction of tension is so as to pull the body.
If a string is inextensible the magnitude of acceleration of any number of masses
connected through string is always same.
If a string is mass less the tension in it is same everywhere. However if the string has
a mass tension at different point will be different.
if there is friction between string pulley ,tension will be different on two sides of the
pulley, but if there is no friction between string and pulley tension will be same on
both sides of the pulley.
Umakanta Sir’s class note Page 3
-: LAWS OF MOTION:-
Point mass: - An object can be considered as a point object if during motion in a given time, it
covers distance much greater than its own size.
Object with zero dimension considered as a point mass.
Point mass is a mathematical concept to simplify the problems.
Force:-
Force is an external effect in the form of a push or pulls which,
(i) Produces or tries to produce motion in a body at rest.
(ii) Stops or tries to stop a moving body.
(iii) Changes or tries to change the direction of motion of the body.
Dimension: Force = mass × acceleration. F = [MLT-2].
Absolute units (i) Newton (S.I. (ii) Dyne (C.G.S)
Gravitational units: (i) Kilogram-force (M.K.S.) (ii) Gram-force (C.G.S).
One Newton is that force which produces an acceleration of 1m/s2 in a body of mass 1
Kilogram. 1N =1kgm/s2.
1 Dyne: One dyne is that force which produces an acceleration of 1cm/s2 in a body of
mass 1g. 1D = 1gcm/s2.
1N = 105 D.
1kgf = 9.8 N.
Out of so many natural forces, for distance 1015 m., nuclear force are strongest while
gravitational force weakest.
F nuclear > Electromagnetic > F gravitational .
INERTIA-
Inherent property of all the bodies by virtue of which they cannot change their state of rest or
uniform motion along a straight line by their own is called inertia.
Inertia is not a physical quantity; it is only a property of the body which depends on
mass of the body.
Inertia has no units and no dimensions
Two bodies of equal mass, one in motion and another is at rest, possess same inertia
because it is a factor of mass only and does not depend upon the velocity.
Inertia means ‘resistance to change’. A body does not change its state of rest or uniform
motion, unless an external force compels it to change that state.
Umakanta Sir’s class note Page 1
,Types of inertia:-
(a) Inertia of rest: - It is the inability of a body to change by itself, its state of rest. This
means a body at rest remains at rest and cannot start moving by its own.
Example:
A person who is standing freely in bus, thrown backward, when bus starts suddenly.
When a bus suddenly starts, the force responsible for bringing bus in motion is also
transmitted to lower part of body, so this part of the body comes in motion along with
the bus. While the upper half of body (say above the waist) receives no force to
overcome inertia of rest and so it stays in its original position. Thus there is a relative
displacement between the two parts of the body and it appears as if the upper part of
the body has been thrown backward.
Note: - If the motion of the bus is slow, the inertia of motion will be transmitted to the
body of the person uniformly and so the entire body of the person will come in motion
with the bus and the person will not experience any jerk.
When a horse starts suddenly, the rider tends to fall backward on account of inertia of
rest of upper part of the body as explained above.
A bullet fired on a window pane makes a clean hole through it while a stone breaks the
whole window because the bullet has a speed much greater than the stone. So its time
of contact with glass is small. So in case of bullet the motion is transmitted only to a
small portion of the glass in that small time. Hence a clear hole is created in the glass
window, while in case of ball, the time and the area of contact is large. During this time
the motion is transmitted to the entire window, thus creating the cracks in the entire
window.
If we place a coin on smooth piece of card board covering a glass and strike the card
board piece suddenly with a finger. The cardboard slips away and the coin falls into the
glass due to inertia of rest.
The dust particles in a blanket fall down when it is beaten with a stick. This is because
the beating sets the blanket in motion whereas the dust particles tend to remain at rest
and hence separate.
(b) Inertia of motion :
It is the inability of a body to change itself its state of uniform motion i.e., a body in
uniform motion can neither accelerate nor retard by its own.
Example:
When a bus or train stops suddenly, a passenger sitting inside tends to fall forward. This
is because the lower part of his body comes to rest with the bus or train but the upper
part tends to continue its motion due to inertia of motion.
Umakanta Sir’s class note Page 2
, An athlete runs a certain distance before taking a long jump. This is because velocity
acquired by running is added to velocity of the athlete at the time of jump. Hence he
can jump over a longer distance
A person jumping out of a moving train may fall forward.
(c) Inertia of direction:-
It is the inability of a body to change by itself direction of motion.
Example:-
When a stone tied to one end of a string is whirled and the string breaks suddenly, the
stone flies off along the tangent to the circle. This is because the pull in the string was
forcing the stone to move in a circle. As soon as the string breaks, the pull vanishes. The
stone in a bid to move along the straight line flies off tangentially.
The rotating wheel of any vehicle throw out mud, if any, tangentially, due to directional
inertia.
When a car goes round a curve suddenly, the person sitting inside is thrown outwards.
Common forces in mechanics:-
(i) Weight: Weight of an object is the force with which earth attracts it. It is also called
the force of gravity or the gravitational force.
(ii) Normal force: When a body is placed on a rigid surface, the body experiences a force
which is perpendicular to the surfaces in contact. Then force is called ‘Normal force’
or ‘Reaction’.
(iii) Tension: The force exerted by the end of taut string, rope or chain against pulling
(applied) force is called the tension. The direction of tension is so as to pull the body.
If a string is inextensible the magnitude of acceleration of any number of masses
connected through string is always same.
If a string is mass less the tension in it is same everywhere. However if the string has
a mass tension at different point will be different.
if there is friction between string pulley ,tension will be different on two sides of the
pulley, but if there is no friction between string and pulley tension will be same on
both sides of the pulley.
Umakanta Sir’s class note Page 3
