**Foucault Pendulum Vocabulary**

Maureen Dooley, B.S.Ed.

Copyright 2004. Permission is granted for classroom use and for non-commercial educational purposes.

**Pendulum**

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.

**Pendulum Bob **

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.

**Pendulum Pivot **

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.

**Position Position**

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."

**Oscillate**

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.

**Period**

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.

**Amplitude**

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**

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**

Acceleration is the rate of change
of velocity. The units are (meters per second) per second or m/sec^{2}
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

**Force **

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.

**Resultant Force **

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**

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.

**Rotation**

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.

**Work**

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.

**Kinetic Energy**

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.

**Potential Energy**

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.