FORCE AND LAWS OF MOTION, CBSE CLASS IX, PHYSICS NOTES PART II

 

CBSE CLASS IX, FORCE AND LAWS OF MOTION, SCIENCE (PHYSICS) NOTES-(PART II)

       FORCE AND LAWS OF MOTION

According to the CBSE Syllabus 2025-26

CBSE Class 9 Science Chapter 9 Force and Laws of Motion Notes

In Class 9 Science Chapter 9 Force and Laws of Motion.

REMAINING TOPICS IN THE CHAPTER

(h) Momentum.                                                                         

• Momentum and Mass.                                                           

• The momentum of an object that is in a state of rest.       

• Unit of momentum.                                                                

• Numericals based on momentum.

(i) Second Law of Motion.                                          

• Proof of Newton's First law of motion from the Second Law. 

(j) Third Law of Motion.                                                           

• Law of conservation of Momentum.

REMAINING OF PART I

Momentum

1. Momentum is the power of motion of an object. The product of velocity and mass is called the momentum. Momentum is denoted by ‘p’.

Therefore, the Momentum of an object = Mass × Velocity 

p = m × v

Where p = momentum, 

m = mass of the object, 

v = velocity of the object.

Some common explanations to understand the momentum:

1. A person gets injured in the case of being hit by a moving object, such as a stone, pebbles, or anything, because of the momentum of that object.

2. Even a small bullet can kill a person when it is fired from a gun because of its momentum due to its velocity.

3.  A person gets injured severely when hit by a moving vehicle because of the momentum of the vehicle due to mass and velocity.

Momentum and Mass

1. Since momentum is the product of mass and velocity (p = m × v) of an object. This means momentum is directly proportional to mass and velocity. Momentum increases with an increase in either mass or velocity of an object.

2. This means if a lighter and a heavier object are moving with the same velocity, then the heavier object will have more momentum than the lighter one.

3. If a small object is moving with great velocity, it has tremendous momentum. And because of momentum, it can harm an object more severely.
Example: a small bullet having a little mass even kills a person when it is fired from a gun.
4. Usually, road accidents prove more fatal at high speeds than at slower speeds. This happens because vehicles running at high speed have greater momentum compared to a vehicle running at a slower speed.

Momentum of an object that is in a state of rest

Let an object with mass m be at rest.

Since the object is at rest, its velocity, v = 0

 Now we know that,

Momentum = mass × velocity

 p = m × 0 = 0

Thus, the momentum of an object at rest, i.e., non-moving, is equal to zero.

Unit of momentum

SI unit of mass = kg

SI unit of velocity = m/s

We know that,

Momentum (p) = m × v

p = kg × m/s  

∴ p = kgm/s

Second Law of Motion


The rate of change of momentum of an object is directly proportional to the applied unbalanced force in the direction of the force.

Δ pt α m (v-u) t

Here, a [ = (v–u)/t ] is the acceleration, which is the rate of change in velocity.

Δ p t α m a

F α m a

F = k m a

For 1 unit of force on a 1 kg mass with an acceleration of 1 m/s², the value of k = 1.

Therefore, F = ma.

 

Mathematical expression

Suppose,
Final momentum, p2 = mv

Mass of an object = m kg

Initial velocity of an object = u m/s

Final velocity of an object = v m/s

∴ Initial momentum, p1 = mu

∴ Change in momentum = Final momentum – Initial momentum

= mv – mu

= m(v – u)

∴ Rate of change of momentum = Change in momentum/Time taken

 Rate of change of momentum p = m(v-u)/t

•  According to the 2nd law, this rate of change is momentum is directly proportional to force.


We know that a = (v - u) / t (From the 1st equation of motion). 

Therefore, F = kma, 

where k is a constant and can be assumed to have a value of 1. 

Thus, F = 1 × m × a = ma. 

The SI unit is kg m/s or Newton.


1 Newton: 


When an acceleration of 1 m/s2 is seen in a body of mass 1 kg, then the

force applied to the body is said to be 1 Newton.

 Proof of Newton’s First Law of Motion from the Second Law

The first law states that if an external force F = 0, a moving body keeps moving with the same velocity, or a body at rest continues to be at rest.
∴ F = 0
We know, F = m(v-u)/t

(i) A body is moving with initial velocity u, then,

m(v-u)/t = 0

v – u = 0

∴ v = u

Thus, the final velocity is also the same.

(ii) A body is at rest i.e., u = 0

Therefore, from above u = v = 0
So, the body will continue to be at rest.

Concept of System

The part of the universe chosen for analysis is called a system.    Everything outside the system is called an environment.

For example, a car moving with constant velocity can be considered a system. All the forces within the car are internal forces, and all forces acting on the car from the environment are external forces, like friction.
 
Conservation of Momentum

The total momentum of an isolated system is conserved.                                    Isolated system = The net external force on the system is zero.

Example: Collision of 2 balls, A and B.
From Newtons 3rd law F_{AB} = -F_{BA}
mAVa−Uat=mBVb−Ubt
mAUA+mBUB=mAVA+mBVB

Law of Conservation of Momentum

When two (or more) bodies act upon one another, their total momentum remains constant (or conserved) provided no external forces are acting.

Initial momentum = Final momentum

Suppose two objects A and B, each of mass m1 and mass m2 are moving initially with velocities u1 and u2, strike each other after time t and start moving with velocities v1 and v2, respectively.

Now,
Initial momentum of object A = m1u1
Initial momentum of object B = m2u2
Final momentum of object A = m1v1
Final momentum of object B = m2v2
 
So,
Rate of change of momentum in A,
F1 = (m1v1 - m1u1)t = m1(v1 - u1)/t  ....(i)
 
Rate of change of momentum in B,
F2 = (m2v2 - m2u2)t =  m2(v2 - u2)/t  ....(ii)
 
We know from the 3rd law of motion,
F1 = −F2
 
So, m1(v1 - u1)/t = -m2(v2 - u2)/t
⇒ m1v1 – m2u2 = −m2v2 + m1u1
⇒ m1u1 + m2u2 = m1v1 + m2v2
Thus, Initial momentum = Final momentum

Third Law of Motion

Newton’s 3rd law states that every action has an equal and opposite reaction. Action and reaction forces are equal, opposite, and acting on different bodies.
 
Applications

(i) Walking is enabled by the 3rd law.
(ii) A boat moves back when we deboard it.
(iii) A gun recoils.
(iv) Rowing of a boat.
 
Inertial and Non-Inertial Frames

A non-inertial frame of reference is a frame of reference in which Newton’s laws of motion do not hold. A non-inertial reference frame is a frame of reference that is undergoing acceleration with respect to an inertial frame. An accelerometer at rest in a non-inertial frame will, in general, detect a non-zero acceleration.
A frame of reference where Newton’s Laws hold is known as an inertial frame of reference. Second Law of Motion




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