Faster than g

An articulated rod and a point particle are dropped from the same height over a table. Friction is neglected. The simulation allows computing fall times and trajectories.

You can select below the initial position of rod and particle by using the slider or entering the initial rod slope as given by its initial angle φ with the horizontal.
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

Compute the rod free end's vertical velocity when its height is z and compare it when particle's velocity at same height. Show that the latter will be smaller for all heights 0 ≤ z < h ≡ L sin φ if and only if φ < arcsin 3^-1/2 = 35.26°.
Use the simulation (after selecting Velocities) to check the result. Start lowering φ: what happens initially, when the heights are still near their initial value?
Check numerically that the rod will reach the table faster than the particle if φ < 47.9°.
Explain why those two results are not contradictory.
You can see the video of the experiment here

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.