Meter Stick Torque Beam, 1J40.20
Topic and Concept:
Statistics of Rigid Bodies, 1J40. Static Torque
Location:
Cabinet: Mechanic (ME)
Bay: C1
Shelf: T
Abstract:
A meter stick, suspended at the center, is used as a torque balance. Different combinations of weights hung at different distances can keep the beam balanced demonstrating how torque works.
Equipment 
Location 
ID Number 



Torque Beam 
ME, Bay C1, Shelf T 

Weights and Weight Hangars 


3/4" Rod and clamps 
Rod and tackle cabinet near main lecture halls 

Important Setup Notes:
 N/A
Setup and Procedure:
 Place apparatus on lecture bench with numbered side facing audience.
 Behind the apparatus, mount a 3/4" rod to the bench with a table clamp.
 To this vertical rod, attach another rod horizontally so that it is about above the apparatus, low enough so that the central loop of the beam can slip onto the rod (this is how we will suspend the beam).
 From each of the outer loops, hang a weight hangar, and load up each with some amount of weight.
 Choose the relative positions on the beam of the weights so that the beam will balance.
 The moment of truth: unhook the chain from the stage left leg of the apparatus. Push the legs out to free the beam. If the previous two steps were completed appropriately, the beam will remain balanced. See photos below for some examples of weight  position combinations.
Cautions, Warnings, or Safety Concerns:
 N/A
Discussion:
There are four torques acting on the beam: that due to gravity (weight of the beam), tension of the suspension string, and each of the two weights. If we set our origin at the 50 cm mark, the torque due to gravity and the tension go to zero. For the torques to balance giving us zero angular acceleration (keeping the beam balanced), we must have
r_{1}·W_{1} = r_{2}·W_{2} > r_{1}·m_{1} = r_{2}·m_{2}
where the r's denote the distance from the center of the beam of each weight hangar and the m's denote the total mass of the weight hangar.
Videos:
References: