# Angular Acceleration

Written by Jerry Ratzlaff on . Posted in Classical Mechanics

Angular 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 $$\large{ lbf-ft }$$ $$\large{ N }$$