Answer to Question #150771 in Physics for Anne

Question

A yo-yo is a solid cylindrical-shaped object wrapped by a string. if the yo-yo has a mass of 0.020kg and a radius of 10cm, find its speed when the string is unwound, moving downward at a distance of 1.0m. The unwinding of the string took place without slipping.

Answer 1

$$mgh=0.5mv^2+0.5I\omega^2\\I=0.5mr^2\\mgh=0.5mv^2+0.5(0.5mr^2)\omega^2\\mgh=0.75mv^2\\\\(9.8)(0.1)=0.75v^2\\v=1.14\frac{m}{s}$$