Momentum (or linear momentum) is a vector quantity equal to the product of mass and velocity: p⃗ = m × v⃗. Its conservation during interactions between objects is a fundamental principle of physics, part of the senior high school physics curriculum.
Discover FizziQ
How to measure it in class
With the FizziQ app, it is possible to study the conservation of momentum during collisions.
Steps:
- Film a collision between two objects (balls, carts on a track)
- Use video tracking to measure the velocities before and after the collision
- Calculate the momenta before: p₁ + p₂
- Calculate the momenta after: p’₁ + p’₂
- Verify the conservation: p₁ + p₂ ≈ p’₁ + p’₂
- Analyze the discrepancies (friction, energy losses)
Scientific activities on this topic
Possible extensions with FizziQ: study of Newton’s cradle and recoil propulsion (water rocket).
Learn more
Vector definition:
Momentum is a vector collinear with velocity: p⃗ = m × v⃗
Its unit is kg·m/s or, equivalently, N·s.
Conservation of momentum:
For an isolated system (no external forces), the total momentum is conserved: Σ p⃗_before = Σ p⃗_after
This is a consequence of Newton’s third law (action-reaction).
Types of collisions:
| Type | Conservation of p | Conservation of Ek |
|---|---|---|
| Elastic | Yes | Yes |
| Inelastic | Yes | No (loss) |
| Perfectly inelastic | Yes | Maximum loss |
Relationship with force:
Newton’s second law can also be written as: F⃗ = dp⃗/dt
Force is the time derivative of momentum.
Formula
Momentum: p⃗ = m × v⃗
Conservation during a collision: m₁v⃗₁ + m₂v⃗₂ = m₁v⃗’₁ + m₂v⃗’₂
Impulse: I⃗ = ∫ F⃗ dt = Δp⃗
where:
- p: momentum (kg·m/s)
- m: mass (kg)
- v: velocity (m/s)
- I: impulse (N·s)
Application examples
- A 20-ton truck at 50 km/h has a momentum of 280,000 kg·m/s
- An electron at 0.1c has a momentum very close to the classical value p = mv: the relativistic correction (gamma factor) is only about 0.5%, hence negligible at this speed
- Cannon recoil illustrates the conservation of momentum
- Airbags increase the collision time to reduce the force experienced (same Δp)
FAQ
Q: Why momentum and not just velocity? A: A truck at 10 km/h is harder to stop than a ball at 100 km/h. Mass matters as much as velocity in collisions.
Q: How to verify the conservation with FizziQ? A: Measure the velocities before and after the collision by video tracking, calculate p = mv for each object, and verify that the sum is conserved (within a few % due to friction).
Q: Is momentum conserved even if the objects deform? A: Yes! Momentum is always conserved in an isolated system. Only kinetic energy can be lost (transformed into deformation, heat…).
Q: Can momentum be created? A: No, it can only be transferred from one system to another. A rocket does not increase the total momentum (rocket + ejected gases), it redistributes it.
Related concepts
Newton’s Third Law - Elastic Collision - Inelastic Collision - Kinetic Energy - Conservation of Energy - Center of Gravity