# 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 formulas

 $$\large{ m = \rho \; V }$$ $$\large{ m = \frac{p}{v} }$$ $$\large{ m = \frac{E}{c^2} }$$ (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

$$\large{ \rho }$$   (Greek symbol rho) = density

$$\large{ d }$$ = 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

$$\large{ p }$$ = momentum

$$\large{ \pi }$$ = 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

$$\large{ V }$$ = volume

## Types of Mass

• Gravitational mass
• Inertial mass
• Invariant mass
• Relativity mass
• Rest mass

## Internal Mass

Internal mass is the mass of an object measured by its resistance to acceleration when a force is applied.  A sphere of the same density has an internal mass to the center.  A sphere of the non-uniform density has a center of mass toward the more dencer of the mass.  A flat mass will have a lower center of gravity with less potential energy.

## Mass Diffusivity

Mass diffusivity, abbreviated as $$D_m$$, is a proportionality constant between the molar flux due to molecular diffusion and the gradient in the concentration of the species.

## Molar Mass

Molar mass, abbreviated as $$M$$, is a physical property.  It is the mass of a given compound equal to its molecular mass in gram.

## 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.

Tags: Equations for Mass