Foucault Pendulum Vocabulary
Maureen Dooley, B.S.Ed.
Copyright 2004. Permission is granted for classroom use and for non-commercial educational purposes.
A system, comprised of an overhead support, from which a string hangs, and an object at the bottom end of the string. The object swings back and forth under the combined influence of gravity and the string.
Any object that hangs on the pendulum string. It can be a toy ball, a bowling ball, or a small car (if the string is string enough). It may be called a "bob" because its vertical position "bobs" up and down while its horizontal motion moves side to side.
The pendulum string is attached to the overhead support by the pivot. The pivot might simply be a knot that ties the string to a hook in the ceiling. For a Foucault pendulum, great care is taken that the pivot allows the pendulum to swing with the same ease in all directions of the compass.
tells where an object is. This can be done with a picture, with words, or with equations. In any case, you have to define a reference location, or "origin," because position is given relative to that location. In all cases you tell two things: The distance from the origin, and the direction that you have to go in order to move from the origin to the object. The distance is measured in meters. The direction can be described by stating an angle between the line from origin to object and a reference direction, such as "east."
For the pendulum, the bob moves back and forth. This back and forth motion is called "oscillation." Its position is said to oscillate back and forth.
The period is the amount of time it takes the bob to make one round trip. If the pendulum bob is pulled back and released, it returns to the hand that released it after a time interval equal to one period. The period of a 1 meter long pendulum is 2 seconds.
The amplitude is the maximum displacement of the bob from its equilibrium position. When the pendulum is at rest, not swinging, it hangs straight down. This position is called the "equilibrium position." It is convenient to take this position as the reference position mentioned as the "origin" in the definition of position. With this origin, the position of the pendulum varies to the left and to the right of the origin. The size of the largest distance away from the origin is called the "amplitude." The bob swings to a distance equal to the amplitude on the left, and next swings to a distance equal to the amplitude on the right.
Velocity tells the rate of change of position. In all cases, you tell two things to specify the velocity: The speed, and the direction of the speed. Speed is measured in meters per second, or m/sec. Direction is described by an arrow pointing in the direction of motion, or by the angle between that arrow and the reference direction used for position.
Acceleration is the rate of change of velocity. The units are (meters per second) per second or m/sec2 Once again, you specify both the size of the acceleration and its direction. If the direction of the acceleration is the same as the direction of the velocity, then the object speeds up. If the direction of acceleration is opposite to the velocity then the object slows down. If the acceleration direction is perpendicular to the velocity direction, then the size of the velocity does not change, but the direction of the velocity does change. Acceleration is different from velocity in a surprising way, best described in three steps:
1) If you give an object a position and leave it alone, it keeps that position.
2) If you give an object a velocity and leave it alone, it keeps that velocity. (This experimental fact is known as Newton's first law of motion.)
3) If you give an object an acceleration and leave it alone, the acceleration drops the zero at the instant you begin leaving it alone.
The only way that an object will accelerate (change velocity) is if it forced to do so. It is sensible to say that the force has a direction, and that direction is the same as the direction of the acceleration. It is sensible to say that a bigger force causes a larger acceleration.
The resultant force is the force that results from the combination of two or more forces. The two forces that act on the pendulum are the force of gravity, pulling straight down, and the force by the pivot, pulling along the string, towards the pivot. Those two forces combine to produce a resultant force. Just as an arrow is pushed forward by the two halves of a bowstring, the pendulum bob is pushed by a resultant force whose arrow "splits" the two component force arrows.
Gravity is the name for a phenomenon that is at once familiar and mysterious. We are pulled so surely towards the earth that we take it for granted; we use the phenomenon to sit, to walk, to run, and to play catch.
Experimentally, an object allowed to fall freely under the influence of gravity is observed to accelerate. Since an object must be forced to accelerate, there must be a force associated with gravity; we call it the force of gravity. The direction of the force of gravity is down. In fact the direction of the force of gravity defines what we mean by "down."
Plane of Oscillation
The two forces, gravity and string define a plane. The same plane is also defined by the pendulum string and the direction down. The resultant force is directed along a line which lies in this plane. The acceleration is also directed along a line that lies in this plane.
If the bob is pulled back and released from rest, the velocity is directed along the same line as the acceleration, and the bob moves along that same line. The path of the bob lies along the plane defined by the string and gravity. This path lies in the plane of oscillation.
Because the string and gravity lie in the plane, it is expected that the plane of oscillation will never change. (The surprise of the Foucault pendulum is that the plane of oscillation changes direction, clockwise in the northern hemisphere, as the day goes by.
If the position of an object changes along a circular path, the object is said to rotate along that circle. The second hand of an analog clock rotates clockwise. The plane of oscillation of a Foucault pendulum rotates clockwise in the northern hemisphere.
People get paid more for trucking food across country that for holding it in place on a shelf. That seems fair, and work is defined for physics in a way that seems similarly fair. Work is the distance that an object is moved, multiplied by the force that pushed it along that distance.
Work can be positive or negative. If the object moves in the same direction as the force (as when a truck accelerates) the work is positive. If the object moves in a direction opposite to the force (as when a truck brakes and slows down) the work is negative.
When the force of gravity pulls down on an object that has been dropped, the force of gravity does positive work on the object.
When a pendulum bob is pulled back and released from rest, the force of gravity does positive work on the bob as it swings down. After the bob goes through the low point it swings back up, and during that upswing, the force of gravity does negative work, bringing it to rest at the top of the swing.
In fact, the bob swings back up to the same height as the release height, so the negative work by gravity on the upswing is the same size as the positive work by gravity on the downswing.
It is as though the work was put into the bob, stored a while, and then taken back. In this picture, the stored work is associated with the velocity of the bob at the bottom of the swing. It turns out that the work is proportional to the square of the speed of the bob.
When converted to speed, the work is said to be converted to Kinetic Energy. Work is said to be converted to kinetic energy, when the work is done to increase the speed.
When the bob is pulled back it is ready to swing down, acquiring kinetic energy. The amount of kinetic energy which it is capable of acquiring is determined by how high the bob was raised when it was pulled back.
Because the bob has potential to gain that kinetic energy, it is said to have "potential energy." It turns out that the potential energy of the bob is proportional to the height of the bob above the lowest point of the swing.