Gravitational Acceleration

Written by Jerry Ratzlaff on . Posted in Classical Mechanics

acceleration gravitationalGravitational acceleration, abbreviated as g, also known as acceleration of gravity or acceleration due to gravity, is the force on an object caused only by gravity.

Acceleration and force are really the same thing.  It all depends on how you measure it.  Acceleration is when you do not care about force but you care about speed.  Force is the change from rest to motion or speed.

On Earth, the gravitational acceleration is a constant:

g = 9.80665 meters/ second2 (metric)

g = 32.1740 feet/ second2 (english)

For other bodies, the acceleration due to gravity, can be calculated below.

 

Formulas that use Gravitational Acceleration

\(\large{ g = \frac{G \; m}{r^2} }\)   
\(\large{ g = \frac{G \; m}{  \left(r \;+\; h_b\right)^2  } }\)  
\(\large{ g = \frac { v_{iy} \;-\; v_y } { t }  }\)   
\(\large{ g = \frac { 2 \; \left(  v_{{iy}^t} \;-\; \Delta y \right)  }{ t^2 }  }\)   
\(\large{ g = \frac{ v_i ^2}{ R } \;  sin \; 2\;\theta }\)  
\(\large{ g = \frac { f_d \; l_p \; v^2 } { 2 \; h_l \; d_p } }\) (Darcy-Weisbach equation)
\(\large{ g =  \frac{ v^2 }{ h_m \; Fr^2 }  }\) (Froude number)
\(\large{ g = \frac{ v^2 }{ 2 \; \left( NPSH \;-\; \frac{ p }{ \gamma } \;+\; \frac{ p_v }{ \gamma }  \right)   }  }\) (net positive suction head)
\(\large{ g = \frac{ p_b \;-\; p_t }{ \rho \; h }  }\)  (Pascal's law
\(\large{ g = \frac {PE} {m \; h}  }\) (potential energy)
\(\large{ g = \frac { 18\; \eta  \; v } { d^2\; \left( \rho_p \;-\; \rho_m \right) } }\) (Stokes' law)

Where:

\(\large{ g }\) = gravitational acceleration

\(\large{ \theta }\) = angle

\(\large{ f_d }\) = Darcy friction factor

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

\(\large{ \rho_m }\) = density of medium

\(\large{ \rho_p }\) = density of particle

\(\large{ d }\) = diameter

\(\large{ Fr }\) = Froude number

\(\large{ h_l }\) = head loss

\(\large{ h_b }\) = height of object from the body surface

\(\large{ h }\) = height of depth of the liquid column

\(\large{ d_p }\) = inside diameter of pipe

\(\large{ m }\) = mass

\(\large{ h_m }\) = mean depth

\(\large{ NPSH }\) = net positive suction head

\(\large{ l_p }\) = lenght of pipe

\(\large{ PE }\) = potential energy

\(\large{ p }\) = pressure

\(\large{ p_b }\) = pressure at bottom of column

\(\large{ p_t }\) = pressure at top of column

\(\large{ r }\) = radius from the planet center

\(\large{ R }\) = range

\(\large{ \gamma }\)  (Greek symbol gamma) = specific weight

\(\large{ t }\) = time

\(\large{ G }\) = universal gravitational constant

\(\large{ p_v }\) = vapor pressure

\(\large{ v }\) = velocity

\(\large{ v_i  }\) = initial velocity

\(\large{ v_{iy} }\) = initial vertical velocity

\(\large{ v_y }\) = vertical velocity in time

\(\large{ \Delta y }\) = vertical displacement in time

\(\large{ \eta }\) = viscosity of medium

 

Tags: Equations for Acceleration Equations for Gravity