Question

A yacht used a cylindrical winder to unwind a cable to release an anchor. Using energy methods,

what is the cable’s acceleration? Explain your answer

Answer 1

Find the angular velocity:

$$mgh=\frac{1}{2}I\omega^2,\\\space\\ \omega=\sqrt\frac{2mgh}{I}.$$

The final velocity of the anchor:

$$v=\omega R=R\sqrt\frac{2mgh}{I}.$$

The cable's acceleration (for the cable of length L):

$$a=\frac{v^2}{2L}=\frac{2mghR^2}{2LI}.$$