# Mass

Written by Jerry Ratzlaff on . Posted in Classical Mechanics

Mass, abbreviated as m, is the amount of matter an object has.  It is the property of a body that causes it to have weight in a gravitational field.  It is expressed as "lbm" in the English Set of units and grams in the SI system of units.  It is sometimes used interchangeably in place of weight. Weight, is a vector quantity that depends on the gravity at a specific location.  Mass on Earth is the same as mass on the moon.  However, the weight on the moon is much less than the weight on the Earth.

Mass is a scalar quantity having direction, some of these include area, density, energy, entropy, length, power, pressure, speed, temperature, volume, and work.

## Mass Types

• Gravitational Mass  -  The mass of an object as measured by its interaction with gravity, it is equal to its inertial mass.
• Invariant Mass  -  The inferred value of the mass is independent of the reference frame in which the energies and momentum are measured so that the mass is invariant.
• Mass Diffusivity  -  A proportionality constant between the molar flux due to molecular diffusion and the gradient in the concentration of the species.
• Molar Mass  -  The mass of a given compound equal to its molecular mass in gram.
• Relativity Mass  -  The mass of a body in motion relative to the observer.
• Rest Mass  -  Rest mass of a body is measured when the body is at rest and motionless and is also relative to an observer moving or not moving.

## Mass formulas

 $$\large{ m = \rho \; V }$$ $$\large{ m = \frac{p}{v} }$$

### Where:

 Units English Metric $$\large{ m }$$ = mass $$\large{lbm}$$ $$\large{kg}$$ $$\large{ \rho }$$   (Greek symbol rho) = density $$\large{\frac{lbm}{ft^3}}$$ $$\large{\frac{kg}{m^3}}$$ $$\large{ p }$$ = momentum $$\large{\frac{lbm-ft}{sec}}$$ $$\large{\frac{kg-m}{s}}$$ $$\large{ v }$$ = velocity $$\large{\frac{ft}{sec}}$$ $$\large{\frac{m}{s}}$$ $$\large{ V }$$ = volume $$\large{ft^3}$$ $$\large{m^3}$$

## Related formulas

 $$\large{ m = \frac{E}{c^2} }$$ (Energy) $$\large{ m = \frac {v_e \; r} {2 \; G} }$$ (Escape Velocity) $$\large{ m = \frac{F}{a} }$$ (Force) $$\large{ m = \frac{F}{g} }$$ (Force) $$\large{ m = \frac {g \; r^2} {G} }$$ (Gravitational Acceleration) $$\large{ m = \frac{I}{\Delta v} }$$ (Impulse Velocity) $$\large{ m = \frac {2 \; KE}{v^2} }$$ (Kinetic Energy) $$\large{ m = \frac{ KE }{ \frac{1}{2} \; v^2 } }$$ (Kinetic Energy) $$\large{ m = \frac {4\; \pi^2\; r_s^3} {G\;t_s^2} }$$ (Kepler's Third Law) $$\large{ m_1 = \frac {F_g \; d^2} {G\; m_2} }$$ (Newton's Law of Universal Gravitation) $$\large{ m_2 = \frac {F_g \; d^2} {G\; m_1} }$$ (Newton's Law of Universal Gravitation) $$\large{ m = \frac {PE} {g \; h} }$$ (Potential Energy)

### Where:

$$\large{ m }$$ = mass

$$\large{ a }$$ = acceleration

$$\large{ d }$$ = distance between objects

$$\large{ E }$$ = energy

$$\large{ v_e }$$ = escape velocity

$$\large{ F }$$ = force

$$\large{ g }$$ = gravitational acceleration

$$\large{ h }$$ = height

$$\large{ I }$$ = impulse velocity

$$\large{ KE }$$ = kinetic energy

$$\large{ m }$$ = mass of object 1 and 2

$$\large{ \pi }$$ = Pi

$$\large{ PE }$$ = potential energy

$$\large{ r }$$ = radius from the planet center

$$\large{ r_s }$$ = radius (satellite mean orbital)

$$\large{ c }$$ = speed of light

$$\large{ t_s }$$ = time (satellite orbit period)

$$\large{ G }$$ = universal gravitational constant

$$\large{ v }$$ = velocity

$$\large{ \Delta v }$$ = velocity differential