Angular acceleration is the rate of change of angular velocity with respect to time. It is a vector quantity and SI unit is radian/sec2.It is generally denoted by the letter $\alpha$. Average Angular Acceleration is given by
$ \alpha = \frac {\Delta \omega}{\Delta t} = \frac {\omega_2 - \omega_{1}}{t}$
Where
$\omega_2$ -> Final Angular velocity
$\omega_1$ -> Initial Angular velocity
t -> time taken
$\alpha$ -> Augular Acceleration
Angular acceleration can also be calculated using different form if Torque and Moment of inertia are given
$ \alpha = \frac {\tau}{I}$
Where
$\tau$ -> Torque
$I$ -> Moment of Inertia
$\alpha$ -> Augular Acceleration
Angular Acceleration Calculator using change in Angular velocity
Note
Enter the values of the three known variables in the text boxes
Leave the text box empty for the variable you want to solve for
Click on the calculate button.
The formula used for solving the question is
$\alpha = \frac {\omega_2 - \omega_{1}}{t}$
Angular Acceleration Calculator
Example of Few questions where you can use this formula Question 1
A object start rotation with angular velocity 2 rad/s and attained a angular velocity 10 rad/s in 4 sec.Find the angular acceleration Solution
Given $\omega _1 =2 \ rad/s$ and $\omega _2 =10 \ rad/s$, t=4 sec, $\alpha$ =?
Using the angular acceleration formula
$ \alpha = \frac {\Delta \omega}{\Delta t} = \frac {\omega_2 - \omega_{1}}{t}= \frac { 10 -2}{4} = 2 / rad/sec^2$
Question 2
A object start rotation with angular velocity 1 rad/s and have angular accleration 5 rad/s2 .Find the angular velocity after 5 sec. Solution
Given $\omega _1 =1 \ rad/s$ and $\omega _2$=?, t=5 sec, $\alpha =5 \ rad/sec^2$
Using the angular acceleration formula
$ \alpha = \frac {\Delta \omega}{\Delta t} = \frac {\omega_2 - \omega_{1}}{t}= \frac { 10 -2}{4} = 2 / rad/sec^2$
Rearranging it
$\omega _2 = \omega _1 + \alpha \times t = 1 + 5 \times 5 = 26 \ rad/sec^2$
How the Angular Acceleration Calculator works
1. if $\omega_2$,$\omega_1$, t is given
Angular Acceleration is calculated as
$\alpha = \frac {\omega_2 - \omega_1}{t}$
2. if $\omega_2$,$\omega_1$, $\alpha$ is given
time is calculated as
$t= \frac {\omega_2 - \omega_1}{\alpha}$
3. if $\omega_2$,$\alpha$, t is given
Initial Angular velocity is calculated as
$\omega_1= \omega_2 - \alpha t$
4. if $\omega_1$,$\alpha$, t is given
Final Angular velocity is calculated as
$\omega_2= \omega_1 + \alpha t$
Angular Acceleration Calculator using Torque and Moment of Inertia
Note
Enter the values of the two known variables in the text boxes
Leave the text box empty for the variable you want to solve for
Click on the calculate button.
The formula used for solving the question is
$\alpha = \frac {\tau}{I}$
Angular Acceleration Calculator
Example of Few questions where you can use this formula Question 1
The total torque exerted on a body is 81 N-m and mass moment of inertia is 9 kg-m2. Calculate Constant Acceleration? Solution
$\tau$=81 N-m, I= 9 kg-m2 ,$\alpha$ =?
Using the angular acceleration -torque formula
$\alpha = \frac {\tau}{I} = \frac {81}{9} = 9 \ rad/sec^2$
Question 2
Calculate the torque if angular acceleration is 6 rad/sec2 and Moment of inertia is 5 kg-m2? Solution
$\tau$=?, I= 5 kg-m2 ,$\alpha =6$ rad/sec2
Using the angular acceleration -torque formula
$\alpha = \frac {\tau}{I}$
Rearranging
$\tau = I \times \alpha= 5 \times 6 =30 \ N-m $
How the Angular Acceleration Calculator using Torque equation works
1. if $\tau$,$I$ is given
Angular Acceleration is calculated as
$\alpha = \frac {\tau}{I}$
2. if $\tau$, $\alpha$ is given
Moment of Inertia(I) is calculated as
$I= \frac {\tau}{\alpha}$
3. if $I$,$\alpha$ is given
Torque is calculated as
$\tau = I \times \alpha$
