- #1
Vrbic
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Homework Statement
Let's have a disk and massless rope tangled in it. One end of rope is tied to the ceiling and the disk is falling freely down. System has one degree of freedom. As a coordinate we can choose angle ##\phi## which says an angle of rotation from the start position. Find from the Lagrange equations of the first kind equation of motion and binding force.
Homework Equations
Lagrange equtions of the first kind:
$$m \ddot x = F_x+ \lambda \frac {\partial f} {\partial x} \\
m \ddot y = F_y+ \lambda \frac {\partial f} {\partial y} $$, where f is binding function
The Attempt at a Solution
I suppose this term ## \lambda \frac {\partial f} {\partial y}## is binding force, but I don't have no idea how to find it.
Next here we use coordinate ##\phi ##, I should transforme y -> ##\phi ##. I suppose diameter of disk ##r ## so ##y=r\phi ##. Do you agree?
I probably know how to solve it other way: ##-ma = -mg +F1, M=F1*R=I*\alpha ##(angular acceleration) ##=mR^2/2*a/R=amR/2## from this I know anything what I need: ##-ma=-mg + am/2 => a=2g/3 ## Is it right?
But I don't know how to solve it through Lagrange equation. Can you advice me?