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.

On Earth, the gravitational acceleration is a constant:

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

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.

formulas that contain the Gravitational Acceleration constant

FORMULA: SOLVE FOR:
\(\large{ g = \frac{G \; m}{r^2} }\)   
\(\large{ g = \frac{G \; m}{  \left(r \;+\; h_b\right)^2  } }\)  
\(\large{ g = \frac { v_{iy} \;-\; v_y } { t }  }\)   
\(\large{ g = \frac { 2 \; \left(  v_{{iy}^t} \;-\; \Delta y \right)  }{ t^2 }  }\)   
\(\large{ g = \frac{ v_i ^2}{ R } \;  sin \; 2\;\theta }\)  
\(\large{ g = \frac { f_d \; l_p \; v^2 } { 2 \; h_l \; d_p } }\) (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:

Units English SI
\(\large{ d }\) = diameter \(\large{ft}\) \(\large{m}\)
\(\large{ d_p }\) = inside diameter of pipe \(\large{ft}\) \(\large{m}\)
\(\large{ f_d }\) = Darcy friction factor \(\large{dimensionless}\)
\(\large{ Fr }\) = Froude number \(\large{dimensionless}\)

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

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

\(\large{\frac{ft}{sec^2}}\) \(\large{\frac{m}{sec^2}}\)
\(\large{ h }\) = height of depth of the liquid column  \(\large{ft}\) \(\large{m}\)
\(\large{ h_b }\) = height of object from the body surface \(\large{ft}\) \(\large{m}\)
\(\large{ h_l }\) = head loss \(\large{ft}\)  \(\large{m}\)
\(\large{ h_m }\) = mean depth \(\large{ft}\) \(\large{m}\)
\(\large{ l_p }\) = length of pipe \(\large{ft}\) \(\large{m}\)
\(\large{ m }\) = mass \(\large{lb_m}\) \(\large{kg}\)
\(\large{ NPSH }\) = net positive suction head \(\large{ft}\) \(\large{m}\)
\(\large{ R }\) = range \(\large{ft}\) \(\large{m}\)
\(\large{ r }\) = radius from the planet center \(\large{ft}\) \(\large{m}\)
\(\large{ PE }\) = potential energy \(\large{\frac{lb_m ft}{s^2}}\) \(\large{N m}\)
\(\large{ p }\) = pressure \(\large{\frac{lb_f}{in^2}}\) \(\large{\frac{N}{m^2}}\)
\(\large{ p_b }\) = pressure at bottom of column \(\large{\frac{lb_f}{in^2}}\) \(\large{\frac{N}{m^2}}\)
\(\large{ p_t }\) = pressure at top of column \(\large{\frac{lb_f}{in^2}}\) \(\large{\frac{N}{m^2}}\)
\(\large{ p_v }\) = vapor pressure \(\large{\frac{lb_f}{in^2}}\) \(\large{\frac{N}{m^2}}\)
 \(\large{ t }\) = time \(\large{seconds}\)
\(\large{ v }\) = velocity \(\large{\frac{ft}{sec}}\) \(\large{\frac{m}{sec}}\)
\(\large{ v_i  }\) = initial velocity \(\large{\frac{ft}{sec}}\) \(\large{\frac{m}{sec}}\)
\(\large{ v_{iy} }\) = initial vertical velocity \(\large{\frac{ft}{sec}}\) \(\large{\frac{m}{sec}}\)
\(\large{ v_y }\) = vertical velocity in time \(\large{\frac{ft}{sec}}\) \(\large{\frac{m}{sec}}\)
\(\large{ \Delta y }\) = vertical displacement in time \(\large{ft}\) \(\large{m}\)
\(\large{ \eta }\) = viscosity of medium \(\large{\frac{lb_f s}{ft^2}}\) \(\large{\frac{N s}{m^2}}\) 
\(\large{ \gamma }\)  (Greek symbol gamma) = specific weight \(\large{dimensionless}\)
\(\large{ \rho }\)   (Greek symbol rho) = density \(\large{\frac{lb_m}{ft^3}}\) \(\large{\frac{kg}{m^3}}\)
\(\large{ \rho_m }\) = density of medium \(\large{\frac{lb_m}{ft^3}}\) \(\large{\frac{kg}{m^3}}\)
\(\large{ \rho_p }\) = particle density \(\large{\frac{lb_m}{ft^3}}\) \(\large{\frac{kg}{m^3}}\)
\(\large{ \theta }\) = angle  \(\large{deg}\) \(\large{rad}\)

Tags: Equations for Acceleration Equations for Gravity