Quick Revision Notes

Class 9 Science - Force and Laws of Motion (बाल तथा गति के नियम)

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### 1. Important Definitions (महत्वपूर्ण परिभाषाएँ)

• Force (बल): A pull or push that acts on an object, which may change its state of rest or uniform motion, or change its direction and shape. (बल वह खिंचाव या धक्का है जो किसी वस्तु की विराम या एकसमान गति की अवस्था को बदलता है या बदलने का प्रयास करता है।)
• Balanced Forces (संतुलित बल): When equal and opposite forces act on a body simultaneously and the net force is zero, they are called balanced forces. They do not change the state of rest or motion of an object.
• Unbalanced Forces (असंतुलित बल): When the resultant of all forces acting on a body is not zero, they are called unbalanced forces. They change the state of motion or shape of the object.
• Inertia (जड़त्व): The natural tendency of an object to resist a change in its state of rest or of uniform motion is called inertia. Mass is a measure of inertia. (वस्तुओं का अपनी विराम अवस्था या गति की अवस्था में परिवर्तन का विरोध करने का गुण जड़त्व कहलाता है।)
• Momentum (संवेग): The momentum of an object is defined as the product of its mass ($m$) and velocity ($v$). It is a vector quantity. (किसी वस्तु का संवेग उसके द्रव्यमान और वेग का गुणनफल होता है।)

### 2. Newton's Laws of Motion (न्यूटन के गति के नियम)

First Law of Motion (गति का प्रथम नियम - Galileo's Law of Inertia)

• Statement: An object remains in a state of rest or of uniform motion in a straight line unless compelled to change that state by an applied force.
• Key Concept: Defines Inertia. Heavy objects have more inertia than lighter objects.

Second Law of Motion (गति का द्वितीय नियम)

• Statement: The rate of change of momentum of an object is proportional to the applied unbalanced force in the direction of force.
• Key Concept: Gives the measure of force.

Third Law of Motion (गति का तृतीय नियम)

• Statement: To every action, there is an equal and opposite reaction.
• Key Concept: Forces always occur in pairs. Action and reaction act on two different bodies.

### 3. Key Formulas & Mathematical Expressions (प्रमुख सूत्र)

• Momentum ($p$): $$p = m \times v$$ (Where $p$ = Momentum, $m$ = Mass, $v$ = Velocity) SI Unit: $\text{kg m/s}$ or $\text{kg m s}^{-1}$

• Change in Momentum: $$\text{Initial Momentum} = m \times u$$ $$\text{Final Momentum} = m \times v$$ $$\text{Change in Momentum} = m(v - u)$$ (Where $u$ = Initial velocity, $v$ = Final velocity)

• Force ($F$) from Second Law: $$F \propto \frac{m(v - u)}{t}$$ $$F = k \cdot m \cdot a$$ (Where $k = 1$ in SI units, $a = \frac{v - u}{t}$ is acceleration)

  $$\mathbf{F = m \times a}$$ (Force = Mass $\times$ Acceleration) SI Unit of Force: Newton ($\text{N}$) or $\text{kg m/s}^2$

• Law of Conservation of Momentum (संवेग संरक्षण का नियम): When two or more bodies act upon one another, their total momentum remains constant (conserved), provided no external unbalanced force is acting.

  $$m_1u_1 + m_2u_2 = m_1v_1 + m_2v_2$$ (Before collision momentum = After collision momentum)

### 4. Important Units (महत्वपूर्ण मात्रक)

(Note: $1 \text{ Newton} = 10^5 \text{ Dyne}$)

### 5. Quick Points to Remember (महत्वपूर्ण बिंदु)

1. Mass is scalar and constant everywhere; Weight is a force and depends on gravity ($W = mg$).
2. Seatbelts are worn in cars to prevent the passenger's forward motion due to inertia when brakes are applied suddenly.
3. A fielder pulls his hands backward while catching a cricket ball to increase the time of catch, which reduces the force of impact (Application of Second Law).
4. Recoil of a gun and propulsion of rockets are based on Newton's Third Law of Motion and the Law of Conservation of Momentum.