Class 9 Physics Chapter 2: Force and Laws of Motion - Formulas

🔹 Class 9 Science – Force and Laws of Motion (Chapter 9)

📘 Key Formulas

Force (F) = Mass (m) × Acceleration (a)
→ F = m × a

Momentum (p) = Mass (m) × Velocity (v)
→ p = m × v

Newton’s Second Law (from momentum):
→ F = (mv - mu) / t

Impulse = Force × Time
→ Impulse = F × t = Change in momentum

Law of Conservation of Momentum:
In a closed system (no external force), the total momentum before and after interaction remains constant.
→ m1u1 + m₂u₂ = m1v1+ m₂v₂
Where:

• m₁, m₂ = masses of two bodies
• u₁, u₂ = initial velocities
• v₁, v₂ = final velocities

Recoil Velocity (v_r):
When a gun fires a bullet, the gun moves backward with recoil velocity due to conservation of momentum.
→ vr = -(m × v) / M
Where:

• m = mass of bullet
• v = velocity of bullet
• M = mass of gun
• v_r= recoil velocity of gun

🔁 Negative sign indicates direction opposite to bullet.

Derivation of Recoil Velocity:
According to the law of conservation of momentum:
Total initial momentum = Total final momentum

Before firing:
Total momentum = 0 (both gun and bullet are at rest)

After firing:
Momentum of bullet = m × v
Momentum of gun = M × vr

Since total momentum is conserved:
0 = m × v + M × vr
⟹ vr = - (m × v) / M

🔁 Negative sign indicates recoil is in the opposite direction to bullet motion.

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📏 SI Units Table

Quantity	Symbol	Formula	SI Unit
Force	F	F = m × a	Newton (N)
Mass	m	–	Kilogram (kg)
Acceleration	a	a = (v - u)/t	m/s2
Momentum	p	p = m × v	kg·m/s
Impulse	–	F × t	N·s (Newton second)

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📏 Unit Conversions of Force

Force	Equivalent	Explanation / Notes
1 Newton (N)	1 kg·m/s2	SI Unit definition of force
1 Newton (N)	105 dyne	CGS Unit conversion
1 kgf (kilogram-force)	9.8 N	Gravitational force on 1 kg mass
1 N	≈ 0.1 kgf	Used to convert between Newton and kgf

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📗 Newton’s Three Laws (Brief)

1. First Law (Law of Inertia): An object remains at rest or in uniform motion in a straight line unless acted upon by an external force.
2. Second Law: The rate of change of momentum is proportional to the applied force.
   → F = m × a
3. Third Law: For every action, there is an equal and opposite reaction.

📌 Key Points

• Force is a vector quantity → has direction and magnitude.
• Momentum is a vector quantity. Its direction is same as the direction of velocity of the body.
• Momentum is conserved in isolated systems.
• 1 Newton = Force needed to give 1 kg mass an acceleration of 1 m/s²

📘 Notes prepared by Horizon Academy | Class 9 CBSE Science