# Law of Conservation of Momentum

Written by Jerry Ratzlaff on . Posted in Classical Mechanics

Law of conservation of momentum states that momentum only moves from one place to another, since it is neither created or destroyed.

## Law of conservation of momentum formulas

 $$\large{ p_i = p_f }$$ $$\large{ p_i + p_f = p_i^{\prime} + p_f^{\prime} }$$ $$\large{ m_i \; v_i + m_f \; v_f = m_i \; v_i^{\prime} + m_f \; v_f^{\prime} }$$

### Where:

 Units English Metric $$\large{ p_f }$$ = the final system's momentum $$\large{\frac{lbm-ft}{sec}}$$ $$\large{\frac{kg-m}{s}}$$ $$\large{ p_i }$$ = the initial system's momentum $$\large{\frac{lbm-ft}{sec}}$$ $$\large{\frac{kg-m}{s}}$$ $$\large{ m_f }$$ = final mass $$\large{lbm}$$ $$\large{kg}$$ $$\large{ m_i }$$ = initial mass $$\large{lbm}$$ $$\large{kg}$$ $$\large{ V_f }$$ = final volume $$\large{ft^3}$$ $$\large{m^3}$$ $$\large{ V_i }$$ = initial volume $$\large{ft^3}$$ $$\large{m^3}$$