Exercise $1.$ The plate OAB forms an equilateral triangle which rotates counterclockwise with increasing speed about point $O.$ If the normal and tangential components of acceleration of the centroid C at a certain instant are $80\frac{m}{se{c}^2}$ and $30\frac{m}{se{c}^2},$ respectively, determine the values of ${}^{}$ and ${}^{}$ at this same instant. The angle is the angle between line $AB$ and the fixed horizontal axis.

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