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. Take the rotation angle of the yo-yo as generalised coordinate and obtain Lagrange's equation.
Find the acceleration of the yo-yo. What upwards acceleration must the support have so that the centre of the yo-yo can remain at rest? Suppose the whole system starts from rest. Find an expression for the total energy E = T + V at time t.