## Physics (10th Edition)

The final angular velocity of the top is $+27.7rad/s$
Since we know the string is wound at a spot where radius is $2cm$, one revolution of the top around that spot equals $2\pi\times2cm=4\pi \ cm$ in length from the string. Therefore, if we unwind the string completely, the number of radians the top will turn is $$\theta=\frac{64cm}{4\pi cm}\times\frac{2\pi rad}{1rev}=32rad$$ We also have $\omega_0=0$ and $\alpha=+12rad/s^2$ $$\omega^2=\omega_0^2+2\alpha\theta=768$$ $$\omega=+27.7rad/s$$