A yo-yo is a uniform solid disc of mass $m$ and radius $R$, with a light string wound round its rim. A hand holds the free end of the string and moves it vertically so that the centre of the yo-yo stays at rest in the air while the yo-yo spins faster and faster, as shown in the figure. Take $g = 10\ \text{m/s}^2$. What must the acceleration of the hand be?

Fig. 1: A yo-yo disc hangs from a string that leaves the right side of its rim and goes straight up to a hand that pulls it up. A dashed horizontal line through the centre of the disc is labelled centre stays at this level.