Newton's Law of Motion: "Everybody
continues in its state of rest or uniform motion on a straight line
unless external force is acted upon it to change its state." Newton's first law of motion is also called as law of inertia. The resistance of a body to change its state
is called inertia.

Inertia of rest

Inertia of motion

Inertia of Direction

Newtons first law of motion gives qualitative defination of force. According to first law of motion, force is
the external agency that tends to change its state of body.

Momentum (Linear Momentum)
The motion contain in a body is called momentum.
The linear momentum of a body is a product
of its mass and velocityb.
It is denoted by p and given by p = mv In vector form, * it is vector quantity * its S.I unit is kgms^{-1} * its dimensional formula is
[MLT^{-1}]

Newton's Second Law of Motion: "The rate of change of linear momentum of a body is doirectly
proportional to the applied force and changes takes places in the
directional of force."

Where k is proportionality constant whose value is equal to 1. Newton second law of motion gives quantilavedefinition of force . according to second law of motion force
is the rate of change of linear momentum of a body. also,
Newton's second law of motion can be expressed as F = ma
or, F = m{(v - u) / t}
or, F = (mv -mu) / t or, F = (final momentum - Initial Momentum) / time taken or, F = (change in
momentum) / time taken
Therefore, Force = Rate of change of momentum

F = dp / dt F = d(mv)/dt F = mdv/dt + vdm/dt F = ma + 0
F = ma

Newton's Third Law of Motion: In every action there is an equal and opposite reaction.

Q. Newton second law of motion is called real law
of
motion: → Newton second law of motion is called real law of motion because both
first law of motion and third law of motion are contained in second law of motion. Newton second
law of motion is called real law of motion:

i) Newton's first law of motion from second law: According to second law of motion, F = ma
If there is absance of external force (f=0) then, 0=ma or, ma = 0 since, m ≠ 0 Therefore, a =
0 Here, zero acceleration means either the body is at rest or moving
with uniform speed. Thus, in absance of external force object cannot
change its state which is first law of motion.

ii) Newton third law of motion from second law:

Consider an isolated system considering
of two object A and B of masses M
_{1} and M_{2} moving in a st. line with velocity u
_{1} and u_{2}( u_{1} > u_{2}) respectively. As shown in above figure , Suppose
they collide and after collision let their velocities become v_{1} v_{2} respectively.

From Newton's second law of motion Force exerted on A = (change in momentum of A) / Time of
impact and force exerted on B = (change in momentum of B) / Time of impact

Now, Total change in momentum, F
_{A} = -F_{B} Which is third law of motion //

Principle of Conservation of Linear
Momentum: →If the system is isolated then the total linear momentum of the system
remains conserve or constant.
i.e. total initial momentum = total final momentum

Proof: From above figure fig(i) , consider an isolated system consisting of two object A and B of masses
m_{1} and m
_{2} moving in a st line with velocity u_{1} and u
_{2} (u_{1} > u_{2}) respectively. as shown in above figure, Suppose they collide and
after collision let, their velociities become v_{1 } and v_{2} respectively.

From Newton's second law of motion, Force exerted on A = (change in momentum of A) / time of
impact F
_{A} = (m_{1}v_{1} - m_{1}u_{1}) / t

Force exerted on B =
(change in momentum of B) / time of impact
F
_{B} =( M_{2}V_{2} - M_{2}U_{2}) / t Now, from newton third law of
motion F
_{A} = -F_{B}
=
i.e total iitial
momentum = total final momentum

Application of Law of Motion:

1) Apparent weight of man lift Answer the weight measured by the weighing machine in the lift is
called apparent weight . A man of mass m handing in the lift and g be the acceleration due to gravity

a) When lift at rest: R+(-mg)=net force R-mg=ma
R-mg=0
R=mg
Therefore,
apparement weight = real weight

b) When lift moving upward and downward with uniform speed : R+(-mg)=net force R-mg=ma
R-mg=0
R=mg
Therefore,
apparement weight = real weight

c) When lift moving upward with uniform acceleration'a' : R+(-mg)=net force R-mg=ma
R=mg+ma
R=m(a+g)
Therefore,
apparement weight is greater then real weight

d) When lift moving downward with uniform acceleration'a' : mg+(-R)=net force mg-R=ma
-R=ma-mg
-R=m(g-a)
R=m(g-a)
Therefore,
apparement weight is smaller real weight

e) If a=g(when lift is moving downward, freefall)
R=m(g-g)
R=m*0
R=0
Therefore,
This is the condition of weightlessness.

f) If a>g
R will be negative
Negative R means the person appears to stick on the ceiling of
lift.

Impulse:

Impulse is a physical quality which measures effect of force. If the force is constant impulse is
expressed as a product of force and time. i.e. Impulse = force × time If the force is variable
then impulse is expressed as product of average force and time up to which force act.
i.e. Impulse = Average Force × time

* It is a vector quantity * Its S.I unit is Kg
ms^{-1} and dimensional formula is [MLT
^{-1}]

From Newton's Second Law of motion Force = (change in momentum) / time Force
× time = change in momentum Impulse = change in momentum

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