Angular Acceleration Problem: Solving for 0.5 rad/s^2 in Fixed Axis Rotation

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I got this problem and I got the answer 0.5 rad/s^2, but it is not the right one. pls help me. thanks

At t=0 wheel rotating about a fixed axis at a constant angular acceleration has an angular velocity of 2 rad/s. Two seconds later it has turned 5 complete revolutions. What is the angular acceleration of this wheel.
 
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What's an equation relating angular displacement with time under uniform angular acceleration? And if you want to know why your answer is wrong you'll have to post what you actually did.
 
Thanks

I figured it out already.
 
To solve this, I first used the units to work out that a= m* a/m, i.e. t=z/λ. This would allow you to determine the time duration within an interval section by section and then add this to the previous ones to obtain the age of the respective layer. However, this would require a constant thickness per year for each interval. However, since this is most likely not the case, my next consideration was that the age must be the integral of a 1/λ(z) function, which I cannot model.
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