I am not interested in an outright answer, I am looking for help understanding w

Question

I am not interested in an outright answer, I am looking for help understanding why I get different results using different formula:

A grindstone used to sharpen tools is rotating at an angular speed fo 8 rad/s when an axe is pressed against it. Because of the torque produced on the grindstone by the force of friction between it and the axe, it comes to rest in four rotations.

Find the frictional force produced, assuming the grindstone is a cylinder of mass 5kg and radius 0.4m. Here is what I've done so far:

Initial angular speed w1 = 8 rad/s

Final angular speed w2 = 0 rad/s

4 rotations equals a total angular dispacement = 25.12 rad

Time taken for this displacement t = / w1 = 3.14 sec

Now, I am wondering why when I use the formula = deltaW/delta T, I get 2.548 rad/s^2, and when I use the formula W2^2 = W1^2 + 2a I get a = 1.274.

How am I using these formula incorrectly and which one is the correct one to use and why?

Explanation / Answer

Time taken for this displacement t = / w1 = 3.14 sec. this is wrong here as w1 is not constant here. it decreases.You take it as constant.

The second formula W2^2 = W1^2 + 2a considered is correct. By using this we are correct.

I think it should be clear now.

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