The Falling Rod Problem

1. Jun 30, 2014

zemansky

1. The problem statement, all variables and given/known data
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?

2. Relevant equations

3. The attempt at a solution
No attempt to solve this problem has been done. I need help to set up the problem!
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

Last edited: Jun 30, 2014
2. Jul 9, 2014

ehild

Hi zemansky, welcome to PF!

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

ehild