Linear momentum

The concept of momentum The momentum of a mass m and velocity v is defined to be p = mv Momentum is a vector quantity whose direction is the same as that of the velocity of the body. Units: kgm/s or Ns

Newton’s second law In terms of momentum: F net = Δp/Δt If the mass of the body is constant, this reduces to the familiar F net = ma

Example questions

Impulse The quantity ∆p = F∆t is called the impulse of the force. Impulse is the area under the curve of a force-time graph and equals the total momentum change of the body.

Example questions

The law of conservation of momentum Given a system of two or more masses, the total momentum of the system is defined as the vector sum of the individual momenta. When no external forces act on a system the total momentum of the system stays the same.

Example questions

Proof of momentum conservation For an isolated system consisting of two bodies A and B. Let the two bodies have masses m a and m b with velocities before the collision v a and v b. As a result of the collision the two bodies change their velocities to u a and u b. Let F stand for the force that A experiences during the collision, which lasted a time Δt.

Two dimensional collisions Momentum is a vector and, under certain circunstances, is conserved. This means that: x- component of total momentum before = x-component of total momentum after y-component of total momentum before = y-component of total momentum after