Classical Mechanics (Kibble & Berkshire) · Problem 11.14
Lagrange's equations and conservation principles — T.W.B. Kibble, F.H. Berkshire
Physics — Mechanics · yo-yo-moving-support
Problem
Yo-yo with moving support A uniform circular cylinder (a yo-yo) has a light inextensible string wrapped around it so that it does not slip. The free end of the string is fastened to a support and the yo-yo moves in a vertical straight line with the straight part of the string also vertical. At the same time the support is made to move vertically having upward displacement Z(t) at time t. Find the acceleration of the yo-yo. What happens if the system starts from rest and the support moves upwards with acceleration 2g?