Relativistic momentum via rest mass and velocity

Momentum (amount of motion) is a vector physical quantity that is a measure of the mechanical movement of a body. The relativistic momentum also takes into account speed limits equal to the speed of light.

Notation:

1. \(c\) (c) is speed_of_light.

Notes:

1. To find rest mass refer to the scalar law.

Links:

1. Wikipedia, derivable from here.

momentum

Vector of the body’s relativistic momentum.

Symbol:

p

Latex:

\({\vec p}\)

Dimension:

momentum

rest_mass

rest_mass of the body.

Symbol:

m_0

Latex:

\(m_{0}\)

Dimension:

mass

velocity

Vector of the body’s velocity. See speed.

Symbol:

v

Latex:

\({\vec v}\)

Dimension:

velocity

momentum_law

p = m_0 * v / sqrt(1 - dot(v, v) / c^2)

Latex:

\[{\vec p} = \frac{m_{0} {\vec v}}{\sqrt{1 - \frac{\left( {\vec v}, {\vec v} \right)}{c^{2}}}}\]

velocity_law

v = p * c / sqrt((m_0 * c)^2 + dot(p, p))

Latex:

\[{\vec v} = \frac{{\vec p} c}{\sqrt{\left(m_{0} c\right)^{2} + \left( {\vec p}, {\vec p} \right)}}\]