Physics Core/AP 1 and 2

Torsion Pendulum

# Building a Torsion Pendulum

A torsion pendulum is the horizontal twisting of some suspeneded "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 experiement is to come up with a formula for the behavior of the pendulum as it depends on the mass. As we vary the mass and its diameter, does the period vary directly? inversely? by some power -- the square or square root?

## Goal: Determine the formula for a torsion pendulumm.

#### 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.
• One of your rods from Torsion Pendulum lab 1, or wire, which can be metal wire or nylon fishing line.
• Stopwatch
• Objects to act as bobs. These should include at least three objects with similar characteristics but different dimensions, which could include (but are not limited to):
• flat disks mounted with the plane of the disk in the vertical dimension
• flat disks mounted with the plane of the disk in the horizontal
• rods that can be suspended by their midpoint horizontally

You need at least two objects of each type, which differ either in dimension or mass. For example, if you test a disk, you should have two disks of the same radius but different masses, or two disks of the same mass but different radii. The point is to figure out whether the radius of the disk or the mass of the disk (or both!) affects the period of the pendulum.

#### Procedures

1. Set up your data table. It should contain columns for trial #, type of object, mass of object, radial dimension (distance from rotational axis to edge), number of oscillations, overall time for oscillations, period for single oscillation.
2. Set up the pendulum with your first object.
3. 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.
4. Repeat with each test object. You may need to use new wire if your original length is deformed by overtwisting.

#### Data Analysis

• Look for patterns between changes in period and changes in radii, mass, or shape of your object.
• 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.