The principle of conservation of linear momentum

1. Understanding the Principle

• Law of Conservation of Linear Momentum:
  • In a closed system (where no external forces act), the total momentum remains constant before and after a collision or explosion.
• Mathematical Expression:

where: $\sum p_{\text{initial}} = \sum p_{\text{final}}$

• $p = mv$ (momentum = mass × velocity)

2. Steps to Solve Conservation of Momentum Problems

1. Choose a direction as positive.

2. Sketch the situation – draw a simple diagram to represent each object.

3. Write down the momentum conservation equation: $\sum p_{\text{initial}} = \sum p_{\text{final}}$

4. Expand the equation according to the type of collision or explosion.

5. Substitute known values into the equation, ensuring correct signs for direction.

6. Calculate the answer.

7. Include units and direction in the final answer.

Important Tips

• Always include units in your answer.
• Positive and negative signs indicate direction.
• Collisions and explosions follow this principle, and most problems involve two objects.