Physics> Linear momentum

Linear momentum is a derivative of the mass and velocity of an object, which is preserved in elastic and inelastic collisions.

Learning challenge

  • Determine the momentum of two colliding objects.

Key points

  • Linear impulse reflects a vector concept characterized by direction and magnitude.
  • Momentum is important because it acts as a stored quantity.
  • The momentum of a system of particles is the sum of their momenta. If the masses of two particles mone and m2, and the velocities vone and v2, then the total impulse: p = pone + p2 = monevone + m2v2


  • Elastic collision is an impact between two bodies, where the total kinetic energy after the collision is equal to the exponent before it. Elastic ones appear in cases where there is no pure transformation of kinetic energy into other forms.
  • Inelastic collision – kinetic energy is not conserved.
  • Conservation is a measurable property of an isolated physical system not to change as it evolves.

Within the limits of classical mechanics, a linear impulse acts as the derivative of the mass and velocity of an object: p = mv (p and v are vectors). It is a vector concept with direction and magnitude. The linear momentum is important because it is a conservative value, that is, in a closed system it will remain stable.

Impulse has a direction, so it can be applied in predicting the resulting direction of objects after impact between them and the speed. The momentum remains stable under inelastic and elastic collisions. If the collision happened on a plane with friction or air resistance, then their impulses will need to be taken into account.

Let’s follow this with an example. The momentum of the systems of two particles is equal to the sum of their momenta. If their masses mone and m2, and the velocities vone and v2, then the total impulse: p = pone + p2 = monevone + m2v2

Don’t forget that momentum and velocity are vector quantities. If the particles are displaced in one direction, then vone and v2 possess one sign.

We choose a plane for the movement of x and y and write the total impulse as:

px = p1x + p2x = monev1x + m2v2x

Py = p1y + p2y = monev1y + m2v2y

In the case of two-dimensionality, the impulse is decomposed into two components, and the equation for each will repeat the above.

Momentum is important because it has the ability to persist.

The total momentum of the system is conserved (we neglect the loss of friction)

Physics Section

  • Linear impulse
  • Momentum, Force and Newton’s Second Law
  • Pulse
Conservation of momentum
  • Internal and external forces
  • Conservation of energy and momentum
  • Sliding collision
  • Elastic collisions in one dimension
  • Elastic collisions in multiple dimensions
  • Inelastic collisions in one dimension
  • Inelastic collisions in multiple dimensions
Rocket engine
  • Rocket propulsion, mass change and momentum
Center of mass
  • Location of the center of mass
  • Center of mass movement
  • Center of mass of the human body
  • Center of gravity and translational motion

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