When Will the Rod Fall without Slipping?

[zemansky]

Homework Statement

A uniform rod of mass M and length L is placed vertically on a flat surface. The coefficient of friction between the rod and the surface is μ. The rod is beginning to fall, initially without slipping. To describe the motion of the rod during this stage:
(a) Write down the Lagrangian and derive the equation of motion for the generalized coordinate
$\phi$.

b) From the Lagrangian derive the expression for the mechanical en- ergy of the system and write down the energy conservation law.

(c) Use Newton’s second law (or D’Alembert’s principle) to derive expressions for the normal (N) and friction (f) forces acting on the rod. Express the answers in terms of $\phi$ only. You can use the results of parts (a) and (b) for this step.

(d) Under what condition will the rod fall all the way to the ground without slipping?

Homework Equations

The Attempt at a Solution

No attempt to solve this problem has been done. I need help to set up the problem!

 

[ehild]

Hi zemansky, welcome to PF!

You need to show what you know. What is "Lagrangian"?

ehild