(i) According to Aristotle, A moving object naturally comes to rest without any external influence or force. Such motions are termed as "natural motion".
(ii) Natural motion is an unforced motion. According to Newtonian mechanics, the natural motion is a uniform rectilinear motion, following its first law of motion. In general relatively, a natural motion may be linear or curved.

(i) It is divided into two branches, namely, statics and dynamics.
(ii) Statics: It deals with the objects which are at rest under the action of forces.
(iii) Dynamics: It is the study of moving objects under the action of forces. Dynamics is further divided as follows:
(a) Kinematics: It deals with the motion of bodies without considering the cause of motion.
(b) Kinetics: It deals with the motion of bodies considering the cause of motion.

(i) This is due to inertia of motion.
(ii) This is because velocity acquired by running is added to the velocity of the athlete at the time of jump.
(iii) Hence he can jump over a longer distance.

Based on the direction in which the force acts, they can be classified into two types as:
(i) Like Parallel forces
(ii) Unlike Parallel forces.

The inherent property of a body to resist any change in its state of rest or the state of uniform motion, unless it is influenced upon by an external unbalanced force is known as 'inertia'.
Types:
(i) Inertia of rest
(ii) Inertia of motion
(iii) Inertia of direction

(i) Gears: A gear is a circular wheel with teeth around its rim. It helps to change the speed of rotation of a wheel by changing the torque and helps to transmit power.
(ii) Seesaw: When the heavier person comes closer to the pivot point (fulcrum) the distance of the line of action of the force decreases. It causes less amount of torque to act on it. This enables the lighter person to lift the heavier person.
(iii) Steering Wheel: A small steering wheel enables you to manoeuore a car easily by transferring a torque to the wheels with less effort.

(i) The natural state of all earthly objects is either the state of rest or the state of uniform motion.
(ii) An object in motion will continue to be in the same state of motion as long as no external force is applied.
(iii) When force is applied on objects, they resist any change in their state. This property of objects is called "inertia".
(iv) When dropped from a height in vacuum, objects of different size, shape and mass fall at the same rate arid reach the ground at the same time.

\(\text { Given } \quad \mathrm{F}_{1} =140 \mathrm{~N}  \)
\(\mathrm{~d}_{1} =40 \mathrm{~cm}=40 \times 10^{-2} \mathrm{~m}  \)
\(\mathrm{~F}_{2} =40 \mathrm{~N}  \)
\(\mathrm{~d}_{2} =?\)
The moment of force on the nut,
\(=F_{1} \times d_{1}=140 \times 40 \times 10^{-2}  \)
\(=56 \ \mathrm{Nm}\)
The same moment of force is required to unscrew the nut,
\(\mathrm{F}_{2} \times \mathrm{~d}_{2}  =40 \times d_2\)
In both cases, moment of forces applied are equal,
F₁ x d₁ = F₂ x d₂
56 = F₂d₂
\(56=40 \times \mathrm{d}_{2}  \)
\(\mathrm{~d}_{2}=\frac{56}{40}=1.4 \mathrm{~m}  \)
\(\mathrm{~d}_{2}=1.4 \mathrm{~m}\)
The spanner with the longer handle requires very less force to unscrew the same nut.

Given \(\mathrm{m}=1 \mathrm{~kg}, \quad \mathrm{v}=10 \mathrm{~m} \mathrm{~s}^{-1}\)
When a ball bounces back with the same speed, the momentum changes from mv to -mv. So, the change in momentum is -2 mv.
Δp = mv - mu
= -mv - mv
\(=-2 \mathrm{mv}=-2 \times 1 \times 10 \)      \([Here \ mu = mv \\ mv = -mv]\)
\(\therefore \Delta P=-20 \mathrm{~kg} \mathrm{~m} \mathrm{~s}^{-1}\)

\(\text {Given } m_{1} : m_{2}=3: 4  \)          
\(a_{2} =12 \mathrm{~m} \mathrm{~s}^{-2}  \)
\(a_{1} =?\)
Using Newton's second law,
\(\mathrm{F} =\mathrm{m \times a}  \)
\(\mathrm{F} =\mathrm{m}_{1} \times a_{1}=3 a_{1}  \)
\(\mathrm{~F} =\mathrm{m}_{2} \times a_{2}=4 \times 12=48 \mathrm{~N}  \)
\(3 a_{1} =48  \)
\(a_{1} =48 / 3=16 \mathrm{~m} \mathrm{~s}^{-2}  \)
\(a_{1} =16 \mathrm{~ms}^{-2}\)
The acceleration produced on the other body is \(16 \mathrm{~m} \mathrm{~s}^{-2}\).

(i) According to Newton's second law, "the force acting on a body is directly proportional to the rate of change of linear momentum of the body and the change in momentum takes place in the direction of the force".
(ii) This law helps us to measure the amount of force. So it is called as law of force'
(iii) Let, "m" be the mass of a moving body, moving along a straight line with an initial speed 'u'.
(iv) After a time interval of 't', the velocity of the body changes to 'v' due to the impact of an unbalanced external force F.
Initial momentum of the body, \( P_{i}=m u \)
Final momentum of the body, \( P_{f}=m v \)
Change in momentum, \( \Delta \mathrm{p}=\mathrm{P}_{\mathrm{f}}-\mathrm{P}_{\mathrm{i}} \)
\(=m v-m u \)
By Newton's second law of motion,
\(\text {Force, } \ F \propto\) rate of change of momentum
\(\mathrm{F} \propto \) change in momentum / time
\(\mathrm{F} \propto \frac{\mathrm{mv}-\mathrm{mu}}{\mathrm{t}}\)
\(\mathrm{F}=\frac{\mathrm{km}(\mathrm{v}-\mathrm{u})}{\mathrm{t}}\)
Here, k is the proportionality constant.
k = 1 in all system of units. Hence,
\(F=\cfrac { m(v-u) }{ t } \)
Since acceleration = change in velocity / time, a = (v-u) / t. Hence, we have
F = m x a
Force = mass x acceleration

(i) Newton's First law: Newton's first law states that, everybody continues to be in its state of rest or the state of uniform motion along a straight line unless it is acted upon by some external force.
(ii) Newton's second law of motion: Newton's second law states that, the force acting on an object is directly proportional to the rate of change of linear momentum of the object and the change in momentum takes place in the direction of force.
(iii) Newton's third law of motion: Newton's third law states that, for every action there is an equal and opposite reaction. They always act on two different bodies.

Definition:
The inherent property of a body to resist any change in its state of rest or the state of uniform motion, unless it is influenced upon by an external unbalanced force, is known as inertia.
Types of Inertia:
(i) Inertia of rest
(ii) Inertia of motion
(iii) Inertia of direction
(i) Inertia of rest: The resistance of a body to change its state of rest is called inertia of rest.
Example: When you vigorously shake the branches of a tree, some of the leaves and fruits are detached and they fall down (Inertia of rest).
(ii) Inertia of motion: The resistance of a body to change its state of motion is called inertia of motion.
Example: An athlete runs some distance before jumping. Because, this will help him jump longer and higher (Inertia of motion).
(iii) Inertia of direction: The resistance of a body to change its direction of motion is called inertia of direction.
Example: When we make a sharp turn while driving a car we tend to lean sideways 'inertia of direction'.