The conical pendulum ties together Newton’s Laws and uniform circular motion in a simple way that is easy to demonstrate. Take a pendulum, and let it swing about gently so that the mass travels in a horizontal circle. Congratulations, you have created a conical pendulum! The conical pendulum is so named because the mass and string sweep out the shape of a cone, where the point of the cone is at the top where you are holding the string.

The motion of the pendulum is analyzed in terms of the vector sum of two forces; the tension in the string and the weight of the ball. The tension in the string has two components; the vertical component serves to balance the force of gravity (weight of the ball) and the horizontal component is unbalanced and provides the inward force (centripetal) required for the circular motion in the horizontal plane. If the ball is swung in a circle at a faster speed, a greater centripetal force must be provided by the horizontal part of the tension. Because the vertical part of the tension still balances the force of gravity on the ball, the faster speed for the ball results in the string making a larger angle with respect to the vertical.

You can see the physics of the conical pendulum at work in some fun applications. If you have ever played tetherball, you are playing with a conical pendulum that has the added complication of a string that varies in length as it winds or unwinds on the pole. Amusement parks often have swing rides that share a lot in common with our simple conical pendulum. The flyball governor (invented by James Watt) regulated the speed of early steam engines: the rotating pendulum was geared to the engine and mechanically coupled to the throttle so when the engine revved too fast or too slow, the changed angle of the pendulum automatically adjusted the throttle to compensate.

A pendulum consisting of a mass attached to a length of string can also serve as a good demonstration accelerometer. Let the mass hang down from the string, hold the other end of the string and move your hand; the pendulum’s position relative to your hand reflects the acceleration of your hand. This simple construction is often used as a measurement tool during physics day at amusement parks.

To learn more about pendulums, check out, Experimenting with a Pendulum.

To learn more about circular motion, check out Circular Motion.

To learn more about circular motion and amusement park physics, check out Centripetal Force: Roller Coaster Loops.

Print Background Essay