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Cavendish Gravity Experiment: How to Measure the Torsion Constant

YouTube Screenshot (https://www.youtube.com/watch?v=l-VRjwe_EHU)

By Andrew Bennett

What Is the Torsion Constant?

The Cavendish gravity experiment involves a balancing of torques on the torsion balance. On the one hand, we have gravity from heavy objects placed near the ends of the balance trying to twist the whole thing in one direction. Opposing that, we have the wire trying to untwist. That "untwisting ability" is described by a number called the torsion constant of the wire. If we are to get a measurable deflection from the Cavendish experiment, we need to use a material for the wire with a very low torsion constant.

Testing the Constant Using a Torsional Pendulum

Testing for the torsion constant directly requires special equipment to measure very small torques. In this video, I test it indirectly by setting up a torsional pendulum (so that the bar on the wire twists back and forth repeatedly). I do this because the relationship between the period of a torsional pendulum and the torsion constant is already known.

When the torsion constant is low, there will be only a small torque trying to twist everything back to the equilibrium position. This results in a back-and-forth twisting motion that takes a long time.  Since our ideal material will have a low torsion constant, we will be looking for a material that gives the torsional pendulum a large period (time to complete one swing).

YouTube Screenshot (https://www.youtube.com/watch?v=l-VRjwe_EHU)

Testing Setup

The setup I'm using here will inherently have fairly long periods. The masses (2.5-pound dumbbell weights) are placed far from the axis of rotation. This gives the system a high rotational inertia. This stabilizes the system but also makes it difficult to make observations, as the whole thing moves so slowly that it is often imperceptible in real-time.

To make these measurements, I set up a camera to take pictures of the system 10 times per minute. Then, I created time lapses from the images. With this method, each time measurement will have an uncertainty of no less than 6 seconds. Given the magnitude of the measurements (ranging from 160 to 807 seconds), this represents a small relative uncertainty. I measured and averaged several swings to reduce this uncertainty.


If viewing via email, click here to watch the video.

What's Next in the Cavendish Demo Series?

In the next video I'll be building and refining an enclosure to minimize the air currents near the device, then creating the mechanism to move the ground weights into position without me having to get into the enclosure. Please subscribe to this blog and my YouTube channel to receive update reminders. And if you have any questions, send them my way. I'm happy to help!

Miss a Post in This Physics Series?

Part 1: Recreating the Cavendish Gravity Experiment: My First 2 Attempts
Part 2: Get to Know the Math Behind the Cavendish Gravity Experiment
Part 3: Cavendish Gravity Experiment: How to Evaluate and Choose the Materials
Part 4: How to Build the Torsion Balance

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