Conical pendulum

A conical pendulum consists of a weight (or bob) fixed on the end of a string or rod suspended from a pivot. Its construction is similar to an ordinary pendulum; however, instead of swinging 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. The conical pendulum was first studied by the English scientist Robert Hooke around 1660 as a model for the orbital motion of planets. In 1673 Dutch scientist Christiaan Huygens calculated its period, using his new concept of centrifugal force in his book Horologium Oscillatorium. Later it was used as the timekeeping element in a few mechanical clocks and other clockwork timing devices. A conical pendulum consists of a weight (or bob) fixed on the end of a string or rod suspended from a pivot. Its construction is similar to an ordinary pendulum; however, instead of swinging 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. The conical pendulum was first studied by the English scientist Robert Hooke around 1660 as a model for the orbital motion of planets. In 1673 Dutch scientist Christiaan Huygens calculated its period, using his new concept of centrifugal force in his book Horologium Oscillatorium. Later it was used as the timekeeping element in a few mechanical clocks and other clockwork timing devices. 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. Two examples were mechanisms to turn the lenses of lighthouses to sweep their beams across the sea, and the location drives of equatorial mount telescopes, to allow the telescope to follow a star smoothly across the sky as the Earth turns. One of the most important uses of the conical pendulum was in the flyball governor (centrifugal governor) invented by James Watt in 1788 which regulated the speed of steam engines during the Steam Age in the 1800s. The playground game tetherball uses a ball attached to a pole by a cord which functions as a conical pendulum, although the pendulum gets shorter as the cord wraps around the pole. Some amusement park rides act as conical 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.