Gregg Grist's Cavendish Experiment Page
Cavendish Experiment
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Isaac Newton's (1642 - 1727) theory of gravitation explained the motion of terrestrial objects and celestial bodies by a force of mutual attraction between all pairs of massive objects proportional to the product of the two masses and inversely proportional to the square of the distance between them.
This can be expressed as

Where G is a constant of proportionality known as the universal gravitation constant. Being that G is very small and that the attraction of the earth is so overwhelming, Newton was not concerned with measuring this constant.

In 1783 Henry Cavendish proposed to measure G by using an apperatus in what has become the Cavendish Experiment.

The main idea is to set up a 'dumbbell' consisting of a rod with two small masses at the ends that is suspended by a fiber. The dumbbell will oscillate in a natural frequency because of the restoring force of the fiber given by:

When a large pair of masses are brought into proximity to the smaller masses the center of the oscillation shifts. This angle can be used along with the period (related to k) to calculate tau, which is also:

Where L is half the length of the dumbbell and r is the distance between the centers of the large and small masses. By setting these two equations equal to each other we can solve for G.
After some manipulation:

Updated 5/10/2002