A \(5.0-\mathrm{kg}\) solid cylinder of radius \(0.25 \mathrm{~m}\) is free to rotate about an axle that runs along the cylinder length and passes through its center. A thread wrapped around the cylinder is pulled straight from the cylinder so as to unwrap with a steady tensile force of \(20 \mathrm{~N}\). As the thread unwinds, the cylinder rotates and there is no slippage between thread and cylinder. If the cylinder starts from rest at \(t_{1}=0\), calculate \((a)\) its rotational velocity at \(t_{\mathrm{f}}=5.0 \mathrm{~s}\) and \((b)\) the angle through which it has turned at \(t_{\mathrm{f}}=5.0 \mathrm{~s}\). Ignore any friction in the axle.