In non-relativistic physics, the relation between momentum and kinetic energy is given by the classical equation:
Kinetic Energy = (1/2) * mass * velocity^2
Momentum = mass * velocity
These two quantities are related but distinct. Kinetic energy represents the energy of an object due to its motion, while momentum represents the object's quantity of motion. In non-relativistic cases, where velocities are much smaller than the speed of light, these two quantities are independent of each other.
However, in relativistic physics, the relationship between momentum and kinetic energy becomes more intricate. The total relativistic energy of an object (including both its rest energy and kinetic energy) is given by the equation:
Total Energy^2 = (rest energy)^2 + (momentum * speed of light)^2
When an object is at rest, its momentum is zero, and the equation simplifies to:
Total Energy = rest energy = mc^2
In this case, the total energy is equivalent to the rest energy, as there is no kinetic energy associated with the object.
When an object is in motion (with nonzero momentum), the total energy incorporates both the rest energy and the relativistic kinetic energy. The relativistic kinetic energy is given by:
Relativistic Kinetic Energy = Total Energy - Rest Energy
This equation demonstrates that as an object's momentum increases, its total energy increases as well. Unlike in non-relativistic physics, where kinetic energy is solely determined by the object's mass and velocity, in relativity, kinetic energy is influenced by both momentum and the object's rest energy.
In summary, the relation between momentum and kinetic energy in non-relativistic physics is straightforward, while in relativistic physics, the total energy of an object, including its rest energy and kinetic energy, is determined by the object's momentum and mass.