Angular Acceleration
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