Modern Physics

# Relativistic Momentum

Equation of momentum determined in Classical Mechanics

In Classical Mechanics, a body of mass

*m*and speed v has momentum*p*defined by the equation shown in the table above. This definition is suitable when the modulus of*v*is small compared to the speed of light. However, when the velocities are “high”, in order to maintain the Principle of Conservation of Momentum, it is verified that*p*must be given by:In the above equation, m _{0} is known as the rest mass. If we do:

The moment equation can be represented as follows:

In order for equation **III** to be equal to equation **I** , we can define the relativistic mass *m* by:

Thus, the equation represents momentum in any case, as long as *m* takes the value of relativistic mass. Note that if v has a much smaller value than c, we have:

In equation II, we see that as the velocity approaches *c* , the denominator of the fraction approaches zero and the momentum becomes infinitely large.