Physics clicker question: falling stick derby

Physics 5A, Fall Semester 2007
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 1/e, Comprehensive Problems 8.97, 8.98

"Falling Meter Sticks--Scaling," 1Q2060.mov
University of Minnesota, School of Physics & Astronomy
http://groups.physics.umn.edu/demo/mechanics/1Q2060.html

Students were asked the following clicker question (Classroom Performance System, einstruction.com) near the end of their learning cycle:

A 1-m stick and a 2-m stick are held vertically upright, and are released such that they begin to fall over at the same time. (This experiment is set-up, but not yet demonstrated yet for the students until after answers have been compiled.)

[0.6 participation points.] Which stick do you think will fall and hit the ground first?
(A) 1 m stick.
(B) 2 m stick.
(C) (They will hit the ground at approximately the same time.)
(D) (I'm lost, and don't know how to answer this.)

Sections 0906, 0907
(A) : 10 students
(B) : 7 students
(C) : 17 students
(D) : 1 student

Correct answer: (A)

The energy conservation equation for a falling stick is:

0 = (1/2)*I*w_f^2 + M*g*(L/2),

where I = (1/3)*M*L^2, such that:

w_f = sqrt(3*g/L).

Thus the shorter stick will have the faster speed as it hits the ground, which can plausibly be reasoned to be the stick that will reach the ground first, before the longer stick does.