Lesson 7 – Momentum & Collisions

Stage 1: Intermediate Complete Notes
Page 1 – Fundamentals of Momentum

Momentum is one of the most important concepts in Mechanics. It connects Laws of Motion, Collisions, Explosions, Centre of Mass, and many real-life situations.

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1️⃣ What is Momentum?

Momentum is a physical quantity that represents the quantity of motion possessed by a body.

Linear Momentum (p) is defined as the product of mass and velocity.

p = m v

Momentum is a vector quantity. Its direction is the same as the direction of velocity.

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2️⃣ Units and Dimensions of Momentum

Since momentum depends on mass and velocity:

• SI unit of mass = kg
• SI unit of velocity = m/s

SI Unit of Momentum: kg m s⁻¹
Dimensions: [M L T⁻¹]

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3️⃣ Physical Meaning of Momentum

Momentum tells us how difficult it is to stop a moving body.

Examples:

• A fast-moving truck is harder to stop than a bicycle.
• A bullet causes more damage due to high momentum.
• A heavy body moving slowly may have the same momentum as a light body moving fast.

👉 Momentum depends on both mass and velocity, not on velocity alone.

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4️⃣ Momentum of a System of Particles

When a system contains more than one particle, the total momentum of the system is defined as the vector sum of individual momenta.

Total Momentum of System:

P = p₁ + p₂ + p₃ + ...

This idea is extremely important in:

• Collisions
• Explosions
• Centre of Mass motion

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5️⃣ Relation Between Momentum and Force

According to Newton’s Second Law, force is related to the rate of change of momentum.

F = dp/dt

If mass is constant:

F = m a

This relation forms the foundation for:

• Impulse
• Collision analysis
• Conservation of momentum

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6️⃣ Important Observations for Exams

✔ Momentum can be zero even if velocity is not zero (system case)
✔ Direction of momentum is always same as velocity
✔ Momentum changes only when force acts

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 Page 1 Summary

✔ Momentum = mass × velocity
✔ Vector quantity
✔ Key link between force and motion
✔ Foundation for collisions and conservation laws

👉 In the next page, we will study Impulse and its physical significance.