Angular Acceleration

Written by Jerry Ratzlaff on . Posted in Classical Mechanics

acceleration angularAngular acceleration, abbreviated as \(\alpha\) (Greek symbol alpha), also called rotational acceleration, of an object is the rate at which the angle velocity changes with respect to time.

 

Angular acceleration formulas

\(\large{ \alpha = \frac { \Delta \omega } { \Delta t }   }\) 
\(\large{ \alpha = \frac { \omega_f \;-\; \omega_i } { t_f \;-\; t_i }  }\)
\(\large{ \alpha = \frac { a_t } { r }   }\) 
\(\large{ \alpha = \frac { \tau } { I }   }\) 

Where:

 Units English Metric
\(\large{ \alpha }\)  (Greek symbol alpha) = angular acceleration \(\large{\frac{deg}{sec^2}}\) \(\large{\frac{rad}{s^2}}\)
\(\large{ \Delta \omega }\)  (Greek symbol omega) = angular velocity differential \(\large{\frac{deg}{sec}}\) \(\large{\frac{rad}{s}}\)
\(\large{ \omega_f }\)  (Greek symbol omega) = final angular velocity \(\large{\frac{deg}{sec}}\)  \(\large{\frac{rad}{s}}\) 
\(\large{ \omega_i }\)  (Greek symbol omega) = initial angular velocity \(\large{\frac{deg}{sec}}\)  \(\large{\frac{rad}{s}}\) 
\(\large{ a_t }\) = tangential acceleration \(\large{\frac{ft}{sec^2}}\) \(\large{\frac{m}{s^2}}\)
\(\large{ I }\) = moment of inertia of a mass or angular mass \(\large{\frac{lbm}{ft^2}}\) \(\large{\frac{kg}{m^2}}\)
\(\large{ r }\) = radius of circular path \(\large{ ft }\) \(\large{ m }\)
\(\large{ \Delta t }\) = time differential \(\large{ sec }\) \(\large{ s }\)
\(\large{ t_f }\) = final time \(\large{ sec }\) \(\large{ s }\)
\(\large{ t_i }\) = initial time \(\large{ sec }\) \(\large{ s }\)
\(\large{ \tau }\)  (Greek symbol tau) = torque  \(\large{ lbf-ft }\) \(\large{ N }\) 

 

Piping Designer Logo 1

Tags: Acceleration Equations