Consider a rod of fixed length L which lies in R^3 with one end of the rod attac
ID: 3122926 • Letter: C
Question
Consider a rod of fixed length L which lies in R^3 with one end of the rod attached to a point on the x axis and the other attached to some point in the y, z plane. (a) Draw a sketch showing a typical position of the rod. Label the end points of the rod by the coordinates (t, 0, 0) and (0, y, z). (b) Write down an equation or system of equations to describe the set X of all configurations of the rod. (c) Let P elementof X be the point t = 0, y = L, z = 0. Using the implicit function theorem explore the possibility of solving for any of the variables t, y or z as a C^1 function of the other two variables in a neighborhood of the point P.Explanation / Answer
Ans-
Since the reaction force at the height is not doing any work, total mechanical energy is conserved.
PE=mgl/2(1cos)PE=mgl/2(1cos)
K=12I0.w2K=12I0.w2
=12ml23.w2=12ml23.w2
12ml2312ml23w2=mglw2=mgl. sin2/2. sin2/2
w=6glsin/2