Momentum

PHYSICS • Form 4 • Chapter 2: Force and Motion I

Momentum

Momentum is a vector quantity that describes the “quantity of motion” of an object. It depends on mass and velocity, and its direction matches the object’s velocity. Objects with larger mass or higher velocity have greater momentum, making them harder to stop.

Learning Objectives

  • Define momentum as a vector quantity.
  • Calculate momentum using the formula \(p = mv\).
  • Apply the principle of conservation of momentum in collisions and explosions.
  • Relate momentum to real-life applications (e.g., fire hoses, rocket launches).

Momentum in Action

See how mass and velocity affect momentum, and how total momentum is conserved in collisions and explosions.

Heavy Lorry vs Light Car

A lorry has much greater momentum than a car at similar speed because of its larger mass.

Lorry 20,000 kg, 22 m s⁻¹ p = 440,000 kg m s⁻¹ Car 2,000 kg, 30 m s⁻¹ p = 60,000 kg m s⁻¹

Conservation in Collisions & Explosions

Total momentum before = total momentum after (no external force).

Collision m₁ m₂ m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂ Rocket Launch gas ↓ rocket ↑ Total momentum conserved

Short Explanation

What is Momentum?

Momentum is a vector quantity that describes the “quantity of motion” of an object. Its direction matches the object’s velocity.

Formula & SI Unit

Momentum is calculated using \(p = mv\), where \(m\) is mass (kg) and \(v\) is velocity (m s\(^{-1}\)). The SI unit is \(\text{kg m s}^{-1}\).

Conservation of Momentum

Total momentum before a collision or explosion equals total momentum after, provided no external force acts: \(m_1u_1 + m_2u_2 = m_1v_1 + m_2v_2\).

Real-Life Applications

Firemen hold hoses tightly to balance the water’s forward momentum (reaction force). In rocket launches, hot gases expelled downward propel the rocket upward, conserving total momentum.

Momentum

\(p = mv\)

where \(p\) = momentum (kg m s\(^{-1}\)), \(m\) = mass (kg), \(v\) = velocity (m s\(^{-1}\)). Direction of momentum = direction of velocity.

Principle of Conservation of Momentum

\(m_1u_1 + m_2u_2 = m_1v_1 + m_2v_2\)

Valid when no external force acts on the system. Applies to both collisions and explosions.

Object Mass (kg) Velocity (m s\(^{-1}\)) Momentum (kg m s\(^{-1}\))
Lorry 20,000 22 440,000
Car 2,000 30 60,000
Bicycle 600 10 6,000

Try to Answer First

Answer in your mind, then press “Check Answer”.

1

A 600 kg bicycle moves at 10 m s\(^{-1}\). What is its momentum?

Check Answer
Answer: \(p = mv\), so \(p = 600 \times 10 = 6{,}000\ \text{kg m s}^{-1}\).
2

A 4 kg ball (5 m s\(^{-1}\)) collides with a 2 kg ball (0 m s\(^{-1}\)). After collision, they move together at 3 m s\(^{-1}\). Is momentum conserved?

Check Answer
Answer: Before: \(4 \times 5 + 2 \times 0 = 20\ \text{kg m s}^{-1}\). After: \((4+2) \times 3 = 18\ \text{kg m s}^{-1}\). No — external friction likely reduced momentum.
3

Why do firemen need multiple people to hold a hose when water gushes out?

Check Answer
Answer: Water has high forward momentum; the reaction force (backward momentum) requires multiple firemen to balance it.

Common Mistakes

  • !Forgetting that momentum is a vector (ignoring direction).
  • !Using speed instead of velocity in \(p = mv\).
  • !Assuming momentum is conserved in all situations (ignoring external forces like friction).

Concept Misunderstandings

Misunderstanding

Momentum is a scalar quantity.

Correct Concept

Momentum is a vector quantity — it has both magnitude and direction, matching the object’s velocity.

Misunderstanding

Only heavy objects have momentum.

Correct Concept

Any moving object has momentum. A tennis ball moving fast has momentum, even though its mass is small.

Misunderstanding

Conservation of momentum applies only to collisions.

Correct Concept

Conservation of momentum applies to both collisions and explosions (e.g., rocket launches), as long as no external force acts.

Summary

  • Momentum (\(p = mv\)) is a vector quantity dependent on mass and velocity.
  • The SI unit of momentum is \(\text{kg m s}^{-1}\).
  • Direction of momentum matches the direction of velocity.
  • Total momentum is conserved in collisions and explosions when no external force acts: \(m_1u_1 + m_2u_2 = m_1v_1 + m_2v_2\).
  • Real-life applications include fire hoses (momentum balance) and rockets (explosion momentum conservation).
  • Heavier or faster objects have greater momentum, making them harder to stop.

Short Activity

Objective: Identify momentum, conservation of momentum, vector quantity and SI unit.

A. Objective Quiz

1 What is the SI unit of momentum?

2 Which statement is true about conservation of momentum?

B. Fill in the Blanks

3 Momentum is a quantity.

4 The formula for momentum is \(p =\) .

C. Matching / Drag and Drop

Drag each term to the correct description. If using a phone, tap the answer first, then tap the matching box.

Term
Momentum
Conservation of Momentum
Vector Quantity
SI Unit of Momentum
Description
1 \(p = mv\)
2 Total momentum before = total after (no external force)
3 Has magnitude and direction
4 \(\text{kg m s}^{-1}\)
 

Keywords

Momentum Conservation of Momentum Vector Quantity SI Unit

Momentum

PHYSICS • Form 4 • Chapter 2: Force and Motion I

Momentum

Momentum is a vector quantity that describes the “quantity of motion” of an object. It depends on mass and velocity, and its direction matches the object’s velocity. Objects with larger mass or higher velocity have greater momentum, making them harder to stop.

Learning Objectives

  • Define momentum as a vector quantity.
  • Calculate momentum using the formula \(p = mv\).
  • Apply the principle of conservation of momentum in collisions and explosions.
  • Relate momentum to real-life applications (e.g., fire hoses, rocket launches).

Momentum in Action

See how mass and velocity affect momentum, and how total momentum is conserved in collisions and explosions.

Heavy Lorry vs Light Car

A lorry has much greater momentum than a car at similar speed because of its larger mass.

Lorry 20,000 kg, 22 m s⁻¹ p = 440,000 kg m s⁻¹ Car 2,000 kg, 30 m s⁻¹ p = 60,000 kg m s⁻¹

Conservation in Collisions & Explosions

Total momentum before = total momentum after (no external force).

Collision m₁ m₂ m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂ Rocket Launch gas ↓ rocket ↑ Total momentum conserved

Short Explanation

What is Momentum?

Momentum is a vector quantity that describes the “quantity of motion” of an object. Its direction matches the object’s velocity.

Formula & SI Unit

Momentum is calculated using \(p = mv\), where \(m\) is mass (kg) and \(v\) is velocity (m s\(^{-1}\)). The SI unit is \(\text{kg m s}^{-1}\).

Conservation of Momentum

Total momentum before a collision or explosion equals total momentum after, provided no external force acts: \(m_1u_1 + m_2u_2 = m_1v_1 + m_2v_2\).

Real-Life Applications

Firemen hold hoses tightly to balance the water’s forward momentum (reaction force). In rocket launches, hot gases expelled downward propel the rocket upward, conserving total momentum.

Momentum

\(p = mv\)

where \(p\) = momentum (kg m s\(^{-1}\)), \(m\) = mass (kg), \(v\) = velocity (m s\(^{-1}\)). Direction of momentum = direction of velocity.

Principle of Conservation of Momentum

\(m_1u_1 + m_2u_2 = m_1v_1 + m_2v_2\)

Valid when no external force acts on the system. Applies to both collisions and explosions.

Object Mass (kg) Velocity (m s\(^{-1}\)) Momentum (kg m s\(^{-1}\))
Lorry 20,000 22 440,000
Car 2,000 30 60,000
Bicycle 600 10 6,000

Try to Answer First

Answer in your mind, then press “Check Answer”.

1

A 600 kg bicycle moves at 10 m s\(^{-1}\). What is its momentum?

Check Answer
Answer: \(p = mv\), so \(p = 600 \times 10 = 6{,}000\ \text{kg m s}^{-1}\).
2

A 4 kg ball (5 m s\(^{-1}\)) collides with a 2 kg ball (0 m s\(^{-1}\)). After collision, they move together at 3 m s\(^{-1}\). Is momentum conserved?

Check Answer
Answer: Before: \(4 \times 5 + 2 \times 0 = 20\ \text{kg m s}^{-1}\). After: \((4+2) \times 3 = 18\ \text{kg m s}^{-1}\). No — external friction likely reduced momentum.
3

Why do firemen need multiple people to hold a hose when water gushes out?

Check Answer
Answer: Water has high forward momentum; the reaction force (backward momentum) requires multiple firemen to balance it.

Common Mistakes

  • !Forgetting that momentum is a vector (ignoring direction).
  • !Using speed instead of velocity in \(p = mv\).
  • !Assuming momentum is conserved in all situations (ignoring external forces like friction).

Concept Misunderstandings

Misunderstanding

Momentum is a scalar quantity.

Correct Concept

Momentum is a vector quantity — it has both magnitude and direction, matching the object’s velocity.

Misunderstanding

Only heavy objects have momentum.

Correct Concept

Any moving object has momentum. A tennis ball moving fast has momentum, even though its mass is small.

Misunderstanding

Conservation of momentum applies only to collisions.

Correct Concept

Conservation of momentum applies to both collisions and explosions (e.g., rocket launches), as long as no external force acts.

Summary

  • Momentum (\(p = mv\)) is a vector quantity dependent on mass and velocity.
  • The SI unit of momentum is \(\text{kg m s}^{-1}\).
  • Direction of momentum matches the direction of velocity.
  • Total momentum is conserved in collisions and explosions when no external force acts: \(m_1u_1 + m_2u_2 = m_1v_1 + m_2v_2\).
  • Real-life applications include fire hoses (momentum balance) and rockets (explosion momentum conservation).
  • Heavier or faster objects have greater momentum, making them harder to stop.

Short Activity

Objective: Identify momentum, conservation of momentum, vector quantity and SI unit.

A. Objective Quiz

1 What is the SI unit of momentum?

2 Which statement is true about conservation of momentum?

B. Fill in the Blanks

3 Momentum is a quantity.

4 The formula for momentum is \(p =\) .

C. Matching / Drag and Drop

Drag each term to the correct description. If using a phone, tap the answer first, then tap the matching box.

Term
Momentum
Conservation of Momentum
Vector Quantity
SI Unit of Momentum
Description
1 \(p = mv\)
2 Total momentum before = total after (no external force)
3 Has magnitude and direction
4 \(\text{kg m s}^{-1}\)
 

Keywords

Momentum Conservation of Momentum Vector Quantity SI Unit