Falling rod

A rod is dropped from rest while its end points remain in contact with the vertical wall and the horizontal table. Friction is neglected and it is assumed the rod remains in a vertical plane. The simulation allows computing fall times and trajectories.

You can select below the initial position of the rod by using the slider or entering the initial height h of its upper end.
Unit length is the rod length L.
Unit time is (L/g)^1/2.
Put the mouse pointer over an element to get information about it.

Activities

Choose an appropriate generalized coordinate to describe the evolution.
Use the latter (and its derivatives) to write the horizontal acceleration of the center-of-mass.
Which will be the geometrical form of the trajectory of a rod point while the upper end remains on the wall?
Write the Lagrangian and a constant of motion
Compute (in function of the initial height h) the height of the upper end when it leaves the wall.
Use the simulation to check your result for different values of h. (The numerical value is displayed in red below the table.)
Compute the velocity of every rod point when they reach the horizontal table.

This is an English translation of the Basque original for a course on mechanics, oscillations and waves.
It requires Java 1.5 or newer and was created by Juan M. Aguirregabiria with Easy Java Simulations (Ejs) by Francisco Esquembre. I thank Wolfgang Christian and Francisco Esquembre for their help.