Gravitational Acceleration

Written by Jerry Ratzlaff on . Posted in Classical Mechanics

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

On Earth, the gravitational acceleration is a constant:

g = 9.80665 \(\large{\frac{rad}{sec^2}}\) (Metric)

g = 32.1740 \(\large{\frac{ft}{sec^2)}}\) (English)

Various formulas that include the constant for the acceleration of gravity, on Earth are below.  Note, these are all arranged to solve for the constant but can also be rearranged to solve for any of the other variables, if they are unknown.

 

Gravitational acceleration formulas

\(\large{ g = \frac{G \; m}{r^2} }\) 
\(\large{ g = \frac{G \; m}{  \left(r \;+\; h_b\right)^2  } }\)
\(\large{ g = \frac { v_{iy} \;-\; v_y } { t }  }\) 
\(\large{ g = \frac { 2 \; \left(  v_{{iy}^t} \;-\; \Delta y \right)  }{ t^2 }  }\) 
\(\large{ g = \frac{ v_i ^2}{ R } \;  sin \; 2\;\theta }\)

Where:

 Units US Metric
\(\large{ g }\) = gravitational acceleration  \(\large{\frac{ft}{sec^2}}\)   \(\large{\frac{m}{s^2}}\)   
\(\large{ \theta }\) = angle \(\large{ deg }\)   \(\large{ rad }\)  
\(\large{ h_b }\) = height of object from the body surface  \(\large{ ft }\) \(\large{ m }\) 
\(\large{ v_i  }\) = initial velocity  \(\large{\frac{ft}{sec}}\)  \(\large{\frac{m}{s}}\)  
\(\large{ m }\) = mass \(\large{ lbm }\)  \(\large{ kg }\) 
\(\large{ r }\) = radius \(\large{ ft }\) \(\large{ m }\)
\(\large{ R }\) = horizontal range of a projectile \(\large{ ft }\)  \(\large{ m }\) 
\(\large{ \gamma }\)  (Greek symbol gamma) = specific weight \(\large{\frac{lbf}{ft^3}}\)   \(\large{\frac{N}{m^3}}\)  
\(\large{ t }\) = time \(\large{ sec }\) \(\large{ s }\)
\(\large{ G }\) = universal gravitational constant \(\large{\frac{lbf-ft^2}{lbm^2}}\)  \(\large{\frac{N -m^2}{kg^2}}\)
\(\large{ v }\) = velocity \(\large{\frac{ft}{sec}}\)  \(\large{\frac{m}{s}}\) 
\(\large{ v_y }\) = vertical velocity in time \(\large{\frac{ft}{sec}}\)   \(\large{\frac{m}{s}}\)  
\(\large{ \Delta y }\) = vertical displacement in time \(\large{ ft }\)  \(\large{ m }\) 

 

Related Gravitational Acceleration constant Formulas

\(\large{ g = \frac { f_d \; l_p \; v^2 } { 2 \; h_l \; d_p } }\) (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

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

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

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

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

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

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

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

\(\large{ v_i  }\) = initial velocity

\(\large{ l_p }\) = length of pipe

\(\large{ m }\) = mass

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

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

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

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

\(\large{ p }\) = pressure

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

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

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

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

\(\large{ v }\) = velocity

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

 

Tags: Equations for Acceleration Equations for Gravity