Momentum relative to the Speed of Light

The page focuses on momentum when traveling close to the speed of light

The Main Idea

Momentum is a property of a moving body; it can be narrowed down to simply mass and velocity (hence, [math]\displaystyle{ p = mv }[/math]). However, the usual momentum equation does not always apply. When traveling near the speed of light, a new equation must be used. This equation was discovered by Albert Einstein in the early 1900's. This discovery revolutionized physics and introduced a new constant, gamma or [math]\displaystyle{ \gamma }[/math], a quantity relating velocity and momentum.

A Mathematical Model

The relative equation for momentum is as follows:
[math]\displaystyle{ p = \gamma * m * v }[/math]
where p is the momentum of the system, m is mass, and v is the velocity. The new constant [math]\displaystyle{ \gamma }[/math] is a bit more complicated.

The equation for [math]\displaystyle{ \gamma }[/math] is as follows:
[math]\displaystyle{ \gamma = \sqrt{\frac{1}{1-\frac{v^2}{c^2}}} }[/math]
where v is again the velocity, and c is the speed of light or [math]\displaystyle{ 3 * 10^8 }[/math]

Examples

Be sure to show all steps in your solution and include diagrams whenever possible

Connectedness

This concept of relativistic momentum affects several different majors. For example, on a quantum physics level, relativistic momentum aids in accurately predicting the position of a particle through a certain period of time.

Relativistic momentum is applicable throughout majors. Hopefully, one day, you'll find its use for you.

History

In 1905, Albert Einstein released his Special Theory of Relativity to the public. This theory set the "speed limit" for the universe at the speed of light. When objects, came closer to the speed of light, many entities are drastically changed (one being momentum). This changed the direction of physics immensely. After this discovery, physicists were better able to predict and calculate momentum on the microscopic scale of fast-moving particles.

See also

Links to different uses of momentum

Further reading

Momentum Principle

Impulse Momentum

Momentum with Respect to External Forces