conical pendulum

Conical pendulums had other uses unrelated to timekeeping.

He also claimed that comets followed elliptical orbits and supported his theory by analogy with the conical pendulum.

It was a conical pendulum governor and one of the final series of innovations Watt had employed for steam engines.

A conical pendulum is a weight (or bob) fixed on the end of a string (or rod) suspended from a pivot.

The conical pendulum was first studied by the English scientist Robert Hooke around 1660 as a model for the orbital motion of planets.

A pair of conical pendulums served as key components in the centrifugal governors used to regulate the operational speed of steam engines.

In the same work, he analysed the conical pendulum, consisting of a weight on a cord moving in a circle, using the concept of centrifugal force.

Building on Watt's design was American engineer Willard Gibbs who in 1872 theoretically analyzed Watt's conical pendulum governor from a mathematical energy balance perspective.

For small angles θ, cos(θ) 1, and the period t of a conical pendulum is equal to the period of an ordinary pendulum of the same length.

The English scientist Robert Hooke studied the conical pendulum around 1666, consisting of a pendulum that is free to swing in two dimensions, with the bob rotating in a circle or ellipse.

We consider a pendulum that is free to swing equally in any direction, so that the bob can move over a spherical surface - an arrangement known as a spherical pendulum or a conical pendulum.

Its construction is similar to an ordinary pendulum; however, instead of rocking back and forth, the bob of a conical pendulum moves at a constant speed in a circle with the string (or rod) tracing out a cone.

During the 1800s, conical pendulums were used as the timekeeping element in a few clockwork timing mechanisms where a smooth motion was required, as opposed to the unavoidably jerky motion provided by ordinary pendulums.

Consider a conical pendulum consisting of a bob of mass m revolving without friction in a circle at a constant speed v on a string of length L at an angle of θ from the vertical.

At the heart of these engines was Watt's self-designed "conical pendulum" governor: a set of revolving steel balls attached to a vertical spindle by link arms, where the controlling force consists of the weight of the balls.