Angular Acceleration

Written by Jerry Ratzlaff on . Posted in Classical Mechanics

Angular Acceleration

Angular acceleration ( \(\alpha\) (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 Formula

\(\alpha = \frac { d \omega } { d t }   \)          \( angular \; acceleration \;=\; \frac { angular \; velocity } { time \; taken }   \)

\(\alpha = \frac { \omega_f  -  \omega_i  } { t_f - t_i }   \)           \( angular \; acceleration \;=\;   \frac {  final \; angular \; velocity  \;-\;  initial \; angular \; velocity  } { final \; time \; taken  \;-\;  initial \; time \; taken } \)         

\(\alpha = \frac { d^2 \theta } { d t^2 }   \)          \( angular \; acceleration \;=\; \frac { angular \; velocity } { time \; taken }   \)       

\(\alpha = \frac { a_t } { r }   \)          \( angular \; acceleration \;=\;  \frac { lineat \; tangential \; path  } {  radius \; of \; circular \; path }   \)    

\(\alpha = \frac { \tau } { I }   \)          \( angular \; acceleration \;=\;    \frac { torgue } { mass \; moment \; of \; inertia }   \)

Where:

\(\alpha\) (Greek symbol alpha) = angular acceleration

\(a_t\) = lineat tangential path

\(\theta\) (Greek symbol theta) = angular rotation

\(r\) = radius of circular path

\(t\) = time taken

\(t_f\) = final time taken

\(t_i\) = initial time taken

\( \tau \) (Greek symbol tau) = torque

\( I \) = mass moment of inertia or angular mass

\(\omega\) (Greek symbol omega) = angular velocity

\(\omega _f\) (Greek symbol omega) = final angular velocity

\(\omega _i\) (Greek symbol omega) = initial angular velocity

 

Tags: Equations for Acceleration