Relativistic Momentum- Correction to Newton's second law

The momentum p of an object of mass m traveling with a velocity v is given by mv. This equation for momentum is a classical or Newtonian one and gives rise to Newton's second law also known as the force law where force is the product of mass and acceleration of a body. But with Einstein's theory of relativity, these equations for momentum and force do not hold well at relativistic speeds. Special relativity forces us to make corrections to the ideas of momentum and force thereby resulting in a correction to Newton's second law. The video introduces the idea of relativistic momentum and goes on to derive the expression for relativistic momentum using the conventional collision problem from the points of view of two different inertial frames of reference in relative motion. The resulting correction term to Newton's second law is also derived. The video forms part of a series of videos on Special Relativity that are being posted on this channel.

[trsomas]

You have derived momentum in terms of relative speed between two frames. But, if I want to find the momentum of a particle in my frame, I should not need to see how fast some other frame is moving relative to me. The relativistic momentum of a particle in a given frame depends on the velocity of the particle in that frame.

Please see this video for step-by-step derivation of relativistic momentum: