# Angular Acceleration calculator

## What is Angular Acceleration

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
$\tau = I \times \alpha$