**Chapter – 7 ****Newton’s laws of motion**

**Newton’s laws of motion**

**Dynamics : ** The branch of physics which deals with the study of cause of motion that is relationship between force and motion and torque and motion is called as dynamics.

**Introduction :**

In daily life, we observe that a non living thing can not change its state without action of external agent. As for example, a pen is kept on the study desk can not move until and unless we displaces it from its initial position. A moving fan can not stop its rotatory motion until it will be switched off. A car driver can not increase car’s speed without using accelerator.

The Greek philosopher Aristotle had researched on motion. He thought that a falling object is affected by its weight and observed that a heavier object falls faster than that of lighter object. According to him Sun, Moon and all other planets revolve around the earth on a set of celestial sphere.

In 16th century, Nicolaus Copernicus published his sun – centered model of universe. He proposed that Earth, Moon and all other planets revolve around the Sun not the Earth and Aristotle’s theory was failed. After that another great scientist came and he was Galileo Galilei. He performed many experiments and conclude that the size of the objects did not matter — the rate of its descent along the ramp remained constant and freely falling objects experience uniform acceleration regardless of mass, as long as extraneous forces, such as air resistance and friction, can be minimized.

A french philosopher René Descartes added new depth and dimension to inertial motion. Fore most among the achievements of Descartes’ physics are the three laws of nature (which, essentially, are laws of bodily motion). His first law states that “ each thing, as far as is in its power, always remains in the same state; and that consequently, when it is once moved, it always continues to move”. Second law states that “all movement is, of itself, along straight lines”.

Now, one of the greatest scientists of the world Issac Newton came and studied René Descartes’s research. He was a great mathematician. His work resulted integral and calculus. His work in optics led to first reflecting telescope. He gave three laws of motion which were published in “Principia Mathematica Philosophiae Naturalis” in 1687.

Now let us discuss each law in details.

**Newton’s First Law Of Motion :**

**Statement : ** “A body at rest or uniform **motion** will continue to be at rest or uniform **motion** until and unless a net external force acts on it.”

**Explanation :** Every object tends to remain in its initial state whether it is state of motion or rest. A fan continues its motion for a few seconds after switching off. Actually the fan is in state of motion and when it is switched off, it tries to maintain its state of motion. Due to this, the fan is moving for a few second after switching off.

A coin is kept on a card board kept on a glass. The coin is at rest on the surface of the card board. Now, let us remove card board suddenly, we may observe that the coin drops into the glass but when the card board is slowly removed, the coin remains on it.

**Concept derived from first law : **

**1 ) Inertia : **

The property of a body by virtue of which it remains in its initial state whether it is state of motion or state of rest, is called as inertia. It can be divided into three parts which are given below.

**a ) Inertia of rest : **Every body tends to remain in its state of rest until and unless an external agent comes into play. This property is termed as inertia of rest. Examples are

- A passenger leans backward on sudden starting of bus.
- A coin kept on the surface drops into glass on sudden removing the card board kept on the glass.
- Dust particles are removed from carpet by beating it.
- A book on the table remains on it until it is removed by someone.
- Fruits fall down due to inertia of rest when the branches of a tree are shaken. Fruits and branches are both at rest, but when branches of trees are shaken, branches starts moving where as fruits remain its state of rest and so separated from the branches and fall down.
- Dust particles on a carpet fall if we beat the carpet with a stick is another example for the inertia at rest. When we beat the carpet with a stick carpet starts moving, but the dust particles remains at its state of rest and separated from the carpet.
- With a quick pull, a table cloth can be removed from a dining table without disturbing dishes on it due to the Inertia of rest. The inertia of rest of the dishes keeps them where they are.

**b ) Inertia of motion :** Every moving object remains in its state of motion until is acted by some external agent. This property is called as inertia of motion. Examples are given below.

- A person trying to get down from a running bus falls forward.
- Passengers travelling by train fall forward when the train applies sudden brake
- Ripe fruits fall from the trees in the direction of wind.
- The swirling of milk in a glass continues even after the stirring is stopped.
- A toy thrown up by a boy inside a moving train moves along with the train.
- When bus applies sharp brakes you fell pushed forward due to inertia of motion.
- A ball thrown upward in a train moving with uniform velocity returns to the thrower because during upward and downward motion, the ball also moves along horizontal with train due to inertia of motion.
- A man jumping from moving bus falls forward due to inertia of motion.
- An athlete runs some distance, before taking a long jump due to inertia of motion.
- A moving bicycle comes to rest after some time if we stop pedalling it.

**c ) Inertia of direction : **Every moving object tries to remain in its initial direction of motion until and unless an external agent comes into play. This property goes to inertia of direction.

Examples are given below.

- Mud through rotating wheels.
- Our protection through umbrella.
- Tangential movement of untied stone.
- When a car makes a sharp turn at a high speed, the driver tends to get thrown to other side due to inertia of direction.
- The spark coming out of a grinding stone are tangential to the rotating stone due to directional inertia.
- It is adviced to tie our luggage kept on the roof of a bus with a rope because luggage can be thrown sideways due to inertia of direction.
- Water is flowing in a particular direction and if you place a rotating wheel particles of water fly of tangentially due to inertia of direction.

**2 ) Force : **

In the above discussion, the term **” external agent “** is used mostly. This external agent is termed as **” FORCE ” ** which can change the state of motion into state of rest or vice versa. It can change the velocity ( increase or decrease ). It can change the direction of motion.

**3 ) Momentum : **

It is the quantity of motion contained in a body. It is measured as the product of mass of the body and velocity of the moving body. It is the vector quantity. Its SI unit is kg-m/sec where as g-cm/sec is its CGS unit.

Momentum = mass * velocity

p = mv ——————————- ( 1 )

where p = momentum

m= mass

v = velocity

**case 1 : **

p = mv

when m = constant, then

p ∝ v

i.e momentum is directly proportional to the velocity of the moving body having constant mass. It means that when the velocity of body of constant mass is increased its momentum will also increase and vice versa.

**case 2 : **

p = mv

when v = constant, then

p ∝ m

i.e momentum is directly proportional to the mass of moving objects having same velocity

**case 3 : **

p = mv

when p = constant, then

mv = constant

m ∝ 1/v

i.e when momentum is kept at constant then the velocity is inversely proportional to its mass or when the bodies of unequal masses have same momentum then the velocity varies inversely to their masses.

**Newton’s second law of motion :**

**Statement : ** ” The rate of change of momentum is directly proportional to the applied force and it acts in the direction of force. ”

**Mathematical formulation :**

Let Δp = change in momentum

Δt = change in time

F = applied force

m = constant mass of the moving object

v = velocity of the moving object

a = acceleration produced in the moving object due to applied force = Δv/Δt

F ∝ Δp / Δt

F = k Δp / Δt

where k is proportionality constant and for simplicity the value of k is chosen as one i.e k = 1

F = Δp / Δt

F= Δ( mv ) / Δt

F = m ( Δv/Δt )

F = ma

Newton’s second law of motion is may be stated as ” if the unbalanced force acts on the moving object, it accelerates in the direction of applied force. ”

From newton’s second law of motion, we get the quantitative definition of force which is given below.

” The product of mass and acceleration is force .”

OR

” The rate of change of momentum is the force.”

**Unit of force :** There is basically two types of unit of force.

i) Gravitational unit

ii) Absolute unit

Gravitational Unit Of Force :

1 ) gram – force OR gram – wt : It is gravitational unit of force in CGS system. The force required to produce 980 cm/sec^{2} in a body of 1 gram, is called as 1 gm – wt or 1 gm – f.

2 ) kg – f OR kg – wt : It is the gravitational unit of force in SI – system. It is the force required to produce 9.8 m/sec^{2} in a body of mass 1 kg.

Absolute unit of force :

1 ) Dyne : It is the absolute unit of force in CGHS – system. It is the force required to produce 1 cm/sec^{2} in a body of mass 1 gm.

2 ) Newton : It is the absolute unit of force in SI – system. It is the force required to produce 1 m/sec^{2} in a body of mass 1 kg.

Relation between gm – wt & kg – wt :

1 kg – wt = 10^{3} gm – wt

OR

1 gm – wt = 10^{-3} kg – wt

Relation between gm – wt & dyne :

1 gm – wt = 1 * 980 gm – cm / sec^{2}

= 980 dyne

Relation between kg – wt & dyne :

1 kg – wt = 1 kg * 9.8 m / sec ^{2}

= 1000 g * 980 cm / sec

= 9.8 * 10 dyn

Relation between newton & dyne :

1 Newton = 1 kg * 1 m/sec ^{2}

= 1000 gm * 100 cm / sec ^{2}

= 10 dyn

**Newton’s Third Law Of Motion : **

**Statement :**** ” **Every **A****ction** has equal ( in magnitude ) and opposite ( in direction ) **Reaction**. ”

**Explanation : ** If we throw a ball towards a wall, it returns after colliding with the wall. Actually, the ball has exerted Action force on the ball and according to newton’s third law of motion the wall also gives a Reaction force ( equal in magnitude and opposite in direction ) on the ball. That’s why the ball is returned.

If a boy jumps from a boat to the shore, the boat moves in the backward direction. Actually the boy’s feet exert an action force on the boat and according to the Newton’s 3rd law of motion, the boat will also exert the reaction force. Therefore, the boat moves backward when the boy jumps from it towards the shore.

A man standing on the ground exerts a force ( Action ) in the downward direction and the ground also give equal and opposite reaction in the upward direction.

**Law of conservation of Momentum :**

” Total linear momentum of an isolated system is remained conserved.”

**Mathematical expression :**

Let

m_{1} = mass of first body

m_{2} = mass of the second body

u_{1} = initial velocity of the first body before collision

u_{2} = initial body of the second body before collision

v_{1} = final velocity of the first body

v_{2} = final velocity of the second body

according to the law of conservation of linear momentum

**m**_{1}u_{1} + m_{2}u_{2} = m_{1}v_{1} + m_{2}v_{2}

_{1}u

_{1}+ m

_{2}u

_{2}= m

_{1}v

_{1}+ m

_{2}v

_{2}

**Practice question :**

**( 1 marks questions : )**

- Define motion.
- Define Rest.
- what do you mean by dynamic physics ?
- State Newton’s first law of motion.
- State Newton’s second law of motion.
- State Newton’s third law of motion.
- State law of conservation of linear momentum.
- what do you mean by linear momentum ?
- Define force.
- which external agent can change the state of an object ?
- what do you mean by inertia ?
- Name the property by virtue of which the direction of a moving object remain unchanged until an external agent can not act on it ?
- Which physical quantity has kg – m/sec
^{2}? - What is the relation between momentum and force ?
- give the relationship between Newton and Dyne.
- Define 1 N.
- Define 1 dyn
- Defin 1 gm – wt .
- Define 1 kg – wt.
- Give the mathematical expression of conservation of linear momentum.
- Give the mathematical expression of Newton’s second law of motion ?
- Which newton’s law give the concept of inertia ?
- Which newton’s law give the concept of force ?
- Which newton’s law give the concept of the quantitative definition of force ?
- Which newton’s law give the concept of linear momentum ?
- Which newton’s law give the relationship between linear momentum and force ?
- On which principles the motion of a rocket depends ?
- What is the relation between momentum and velocity of a moving object ?
- What is the relation between momentum and mass of a moving object ?
- Draw the p versus v graph.
- Draw the p vs m graph.
- Draw the p vs F graph.
- What is the absolute unit of force ?
- Two bodies with the same mass moving with different velocities, which has greater momentum ?
- is it easy to walk on sand ?

**( 2 marks questions )**

##### Explain the following :

- A passenger leans backward on sudden starting of bus.
- A coin kept on the surface drops into glass on sudden removing the card board kept on the glass.
- Dust particles are removed from carpet by beating it.
- A book on the table remains on it until it is removed by someone.
- Fruits fall down due to inertia of rest when the branches of a tree are shaken. Fruits and branches are both at rest, but when branches of trees are shaken, branches starts moving where as fruits remain its state of rest and so separated from the branches and fall down.
- Dust particles on a carpet fall if we beat the carpet with a stick is another example for the inertia at rest. When we beat the carpet with a stick carpet starts moving, but the dust particles remains at its state of rest and separated from the carpet.
- With a quick pull, a table cloth can be removed from a dining table without disturbing dishes on it due to the Inertia of rest. The inertia of rest of the dishes keeps them where they are.
- A person trying to get down from a running bus falls forward.
- Passengers travelling by train fall forward when the train applies sudden brake
- Ripe fruits fall from the trees in the direction of wind.
- The swirling of milk in a glass continues even after the stirring is stopped.
- A toy thrown up by a boy inside a moving train moves along with the train.
- When bus applies sharp brakes you fell pushed forward due to inertia of motion.
- A ball thrown upward in a train moving with uniform velocity returns to the thrower because during upward and downward motion, the ball also moves along horizontal with train due to inertia of motion.
- A man jumping from moving bus falls forward due to inertia of motion.
- An athlete runs some distance, before taking a long jump due to inertia of motion.
- A moving bicycle comes to rest after some time if we stop pedalling it.
- Mud through rotating wheels.
- Our protection through umbrella.
- Tangential movement of untied stone.
- When a car makes a sharp turn at a high speed, the driver tends to get thrown to other side due to inertia of direction.
- The spark coming out of a grinding stone are tangential to the rotating stone due to directional inertia.
- It is adviced to tie our luggage kept on the roof of a bus with a rope because luggage can be thrown sideways due to inertia of direction.
- Water is flowing in a particular direction and if you place a rotating wheel particles of water fly of tangentially due to inertia of direction.