A particle rotates along a circle of radius \( R=\sqrt{2} \mathrm{~m} \) with an angular acceler...

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A particle rotates along a circle of radius \( R=\sqrt{2} \mathrm{~m} \) with an angular acceleration \( \alpha=\frac{\pi}{4} \mathrm{rad} / \mathrm{s}^{2} \) starting from rest. Calculate the magnitude of average velocity of the particle over the time it rotates a quarter circle.
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