A yo-yo is a physics lab that you can fit in your pocket. If a yo-yo rolls down its string for a distance h. it loses potential energy in amount but gains kinetic energy in both transnational and rotational forms. As it climbs back up, it loses kinetic energy and regains potential energy.
In a modem yo-yo, the string is not tied to the axle but is looped around it. When the yo-yo “hits” the bottom of its string, an upward force on the axle from the string stops the descent. The yo-yo then spins, axle inside loop, with only rotational kinetic energy. The yo-yo keeps spinning (sleeping) until you wake it by jerking on the string, causing the string to catch on the axle and the yo-yo to climb back up.
To find an expression for the linear acceleration acorn of a yo-yo rolling down a string, we could use Newton’s second law just as we did for the body rolling down a ramp. The analysis is the same except for the following:
1. Instead of rolling down a ramp at angle () with the horizontal, the yo-yo rolls down a string at angle with the horizontal.
2. Instead of rolling on its outer surface at radius R, the yo-yo rolls on an axle of radius .
3. Instead of being slowed by frictional force I; the yo-yo is slowed by the force f on it from the string.