A yo-yo is composed of two disks of radius \(a\), with many layers of string wrapped around the axle. The radial distance from the center of the axle to the top layer of string at any instant is \(b\). With the end of the string wrapped around your finger and \(b / a \approx 1\), you let the yo-yo drop, unwinding string and ultimately spinning pretty fast when it reaches the bottom of the string \((b / a \approx 0)\). You begin to wonder how the motion of the yo-yo as the string unwinds depends on the value of b.