The initial angular frequency \(\displaystyle\omega_{{{0}}}={0}\)

The Final angular frequency \(\displaystyle\omega_{{{f}}}={20}{r}\pm\)

\(\displaystyle={20}\cdot{\left({2}\frac{\pi}{{60}}\right)}{r}{a}\frac{{d}}{{s}}\)

The time taken t = 8s

The radius of the merry-go-round R = 2m

Mass of merry-go-round M = 600kg

Mass of child m = 20kg

Therefore the angular acceleration \(\displaystyle\alpha=\triangle\frac{\omega}{\triangle}{t}\)

The Torque required \(\displaystyle{T}={I}_{{{s}{y}{s}{t}{e}{m}}}\cdot\alpha\)

\(\displaystyle={\left({I}_{{{m}{e}{r}{r}{y}}}+{I}_{{chi{l}{d}{r}{e}{n}}}\right)}\cdot\alpha\)

\(\displaystyle={\left[{\left(\frac{{1}}{{2}}\right)}{M}_{{{m}{e}{r}{r}{y}}}{R}^{{{2}}}+{2}{m}_{{chi{l}{d}}}{R}^{{{2}}}\right]}\cdot\alpha\)

substitute the values and calculate the Torque.

b) The Force required at the edge is calculated from the torque

\(\displaystyle{T}={F}_{{{p}{e}{r}{p}{e}{n}{d}{i}{c}\underline{{a}}{r}}}\cdot{R}{a}{d}{i}{u}{s}\)

Or \(F=\frac{t}{R}\)