Rotational analysis!

Classical Mechanics Level pending

A solid sphere of mass \(2 Kg\) and Radius \(2\)metre is rotating clockwise as well as translating on a rough horizontal surface of friction coefficient ,\(\mu = 0.9\).

A force at a height \(\large\ \frac{4}{3}\) from centre of sphere is applied of magnitude \(84\)N. \(a\) is the linear acceleration of centre of mass of sphere, its value is \(3\)m/\(s^2\).

Friction is enough to prevent slipping.

Find sphere's angular acceleration in \(rad/(s^2)\).

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