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Angular Acceleration Calculator
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Angular acceleration is the rate of change of angular velocity with respect to time. Angular Acceleration Calculator helps to calculate the instantaneous acceleration with respect to time. It also calculates the torque, moment of inertia or angular acceleration if any of the two quantities are given.

Default function is given in the calculator to calculate the instantaneous acceleration below. When you click on "Evaluate", the calculator will substitute the value in the formula given in the steps and you will get the instantaneous acceleration.
 

Steps for Angular Acceleration Calculator

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Step 1 :  

Analyze the problem. List the given parameters.


 



Step 2 :  

If you are interested in calculating torque or Moment of inertia we use the formula


$\alpha$ = $\frac{\tau}{I}$


where I = Moment of inertia and


$\tau$ = torque.


If you are finding Instantaneous angular acceleration, we use formula


$\alpha$ = $\frac{d^{2} \theta}{dt^{2}}$


substituting the values you will get the desired answer.



Problems on Angular Acceleration Calculator

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  1. Calculate the angular acceleration if torque is 3 rad/s and Moment of inertia is 5 kg m2/rad2.


    Step 1 :  

    given: $\tau$ = 3 rad/s,


    I = 5 kg m2/rad2


     



    Step 2 :  

    The angular acceleration is given by


    $\alpha$ = $\frac{\tau}{I}$


                  = $\frac{3}{5}$



    Answer  :  

    The angular acceleration $\alpha$ = 0.6 rad/s2



  2. An object is rotating according to the function $\theta$ (t) = 3t3 + t2, find the instantaneous acceleration when t = 2 seconds?


    Step 1 :  

    given: $\theta$ (t) = 3t3 + t2



    Step 2 :  

    $\frac{d^{2} \theta}{dt^{2}}$ = 18t.
     
    Hence when t = 2 seconds,


    $\frac{d^{2} \theta}{dt^{2}}$ = 36 s


     



    Answer  :  

    Instantaneous acceleration $\alpha$ = 36 s.



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