Building a Torsion Pendulum

A torsion pendulum is the horizontal twisting of some suspended "bob" first to one side, then the other, as it hangs from a vertical support. Review the Torsion Pendulum Experiment at the University of Toronto to see some of the factors involved.

Our goal in this experiment is to come up with a formula for the behavior of the pendulum. As we vary the length of the pendulum, does the period vary directly? inversely? by some power -- the square or square root? If we vary the mass of the rod, or its thickness, how does the period change?

Goal: Determine the formula for a torsion pendulum: factors in the rod.

Equipment and Materials

You will need to duplicate to some extent the apparatus shown in the University of Toronto summary.

Fixed point from which to suspend the pendulum.
2-4 rods of different diameters but the same material (e.g., two wooden dowels or three zinc rods) and length.
Pliers with which to twist the rod.
Protractor or other measure set to limit how far you twist to rod.
Stopwatch
A single mass which can be fastened to the end of the rod.

Procedures

Measure the length and diameter of your rods, and identify the materials they are made of (if possible).
Set up your data table. It should contain columns for trial #, identity of rod, length of rod, diameter of rod, number of oscillations, overall time for oscillations, period for single oscillation.
Set up the pendulum with your first rod. Fix the rod where it is suspended as close to the top of the rod as possible.
Twist the object a set amount, release it (starting your timer), and time the total number of seconds for 10 oscillations (you may want to use more or less depending on your sense for the most accurate reading). Record your data.
Repeat with your other rods, collecting and recording your data.
With the first rod, fix the rod at a point at least 25% (1/4) of the way from the top, so that the region free to twist is significantly shorter. Twist the same amount as your first attempt and record the times involved.
Repeat your observations on a shortened rod with your remaining rods.

Data Analysis

Look for patterns between changes in period and changes in radii and length of your rod.
Check the moment of inertia tables in chapter 8 of your text for clues about how radii and mass affect the moment of inertia for different shapes.

Report

Your report should include a description of your equipment and methods, your data table, and your determination of the factors on which the period of the torsion pendulum depends.

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