# Law of Conservation

Written by Jerry Ratzlaff on . Posted in Classical Mechanics

Law of conservation, also called conservation law, states that the total energy of an isolated system remains constant and its physical properties are conserved over time.

## Law of conservation of angular momentum

Law of conservation of angular momentum states the angular moment of a system of particles around a fixed point is conserved if there is no net external torque around that point.

### law of conservation of angular momentum formulas

 $$\large{ \Rightarrow\; \Delta L = 0 }$$ $$\large{ \Rightarrow\; \Delta L_i = L_f }$$ $$\large{ L = I \; \omega }$$

### Where:

 Units English Metric $$\large{ L }$$ = angular momentum (rotational momentum) $$\large{\frac{lbm-ft^2}{sec}}$$ $$\large{\frac{kg-m^2}{s}}$$ $$\large{ \omega }$$  (Greek symbol omega) = angular velocity $$\large{\frac{rad}{sec}}$$ $$\large{\frac{rad}{s}}$$ $$\large{ L_f }$$ = final angular momentum $$\large{\frac{lbm-ft^2}{sec}}$$ $$\large{\frac{kg-m^2}{s}}$$ $$\large{ L_i }$$ = initial angular momentum $$\large{\frac{lbm-ft^2}{sec}}$$ $$\large{\frac{kg-m^2}{s}}$$ $$\large{ I }$$ = moment of inertia $$\large{ lbm-ft^2 }$$ $$\large{ kg-m^2 }$$

## Law of conservation of electric charge

Law of conservation of electric charge states the sum of all the electric charges in any closed system is constant.

## Law of conservation of energy

Law of conservation of energy, also called conservation of energy, states that energy cannot be created or destroyed, but may be changed from one form to another.

## Law of conservation of linear momentum

Law of conservation of linear momentum states if the net external force acting on a system of bodies is zero, then the momentum of the system remains constant.

### law of conservation of linear momentum formula

 $$\large{ \overrightarrow{p} = m \; \overrightarrow{v} }$$

### Where:

 Units English Metric $$\large{ m }$$ = mass $$\large{lbm}$$ $$\large{kg}$$ $$\large{ \overrightarrow{p} }$$ = linear momentum $$\large{\frac{lbm-ft}{sec}}$$ $$\large{\frac{kg-m}{s}}$$ $$\large{ \overrightarrow{v} }$$ = linear velocity $$\large{\frac{ft}{sec}}$$ $$\large{\frac{m}{s}}$$

## Law of conservation of mass

Law of conservation of mass states in a closed system, the mass of the system cannot change over time.

### law of conservation of mass formula

 $$\large{ \frac{ \partial \rho }{ \partial t } + \triangledown \; \left( \rho \; v \right) = 0 }$$

### Where:

 Units English Metric $$\large{ \rho }$$   (Greek symbol rho) = density $$\large{\frac{lbm}{ft^3}}$$ $$\large{\frac{kg}{m^3}}$$ $$\large{ \partial }$$ = divergence - - $$\large{ v }$$ = flow velocity field $$\large{\frac{ft}{sec}}$$ $$\large{\frac{m}{s}}$$ $$\large{ t }$$ = time $$\large{ sec }$$ $$\large{ s }$$

## Law of conservation of mass-energy

Law of conservation of mass energy states that the energy can change from one form to another, but it cannot be created or destroyed.

## Law of conservation of matter

Law of conservation of matter states that the mass of an object or collection of objects never changes over time, even when the matter changes form.

## Law of conservation of mechanical energy

Law of conservation of mechanical energy states the total mecanical energy in a system remains constant as long as the only force acting are conservative forces.

### law of conservation of mechanical energy formula

 $$\large{ PE_i + KE_i = PE_f + KE_f }$$

### Where:

 Units English Metric $$\large{ KE_f }$$ = final kinetic energy $$\large{ lbf-ft }$$ $$\large{J}$$ $$\large{ PE_f }$$ = final potential energy $$\large{ lbf-ft }$$ $$\large{J}$$ $$\large{ KE_i }$$ = initial kinetic energy $$\large{ lbf-ft }$$ $$\large{J}$$ $$\large{ PE_i }$$ = initial potential energy $$\large{ lbf-ft }$$ $$\large{J}$$

## Law of conservation of momentum

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 $$\large{ft^3}$$ $$\large{m^3}$$ 