Have you ever ridden one of those tilt-a-whirl rides at a carnival? You know how you feel
like your being pushed up against the outside edges of the barrel? Well, when asked why you felt
that way many people would probably say that it has to do with centrifugal force. In reality,
centrifugal force is an imaginary force.
To understand the real reason you feel like that, we need to talk a little about circular
motion. We learned from Newton's First Law that an object always wants to go in a straight line
unless acted upon by an unbalanced outside force. In circular motion, the object wants to
continue in a straight line but is constantly being pulled in by some force, creating the shape
of a circle. That force that keeps pulling on the object is called the centripetal force. The
combination of wanting to fly off in a straight line and being pulled by the centripetal force
creates the feeling that you are being pushed against the outside of the circle. That feeling is
what we have labeled centrifugal force.
If an object were to all of the sudden be released, where would it go? Since an object wants
to go in a straight line, it would continue straight from the moment in time that it was released,
which means it would fly off tangent to the circle. Tangent means perpendicular to the radius.
Guess what? F = m * a also works for centripetal acceleration. It does, or
course, require a few minor modifications. The new equation is FC = m * aC. The subscripted
"C" after the "a" let's you know that you are dealing with centripetal acceleration. Centripetal
acceleration differs from linear and angular acceleration for one main reason.
As you know, velocity is a vector, which means it has both magnitude and direction. So far,
in acceleration we have only been changing the magnitude. Well, in centripetal acceleration, it
is the direction that is constantly changing. The equation for centripetal acceleration, like
the equation for average velocity, has two parts.
AC = v2 / r = 
2 * r
To help this sink in, we'll do a sample problem.
What is the centripetal acceleration of a satellite that revolves around the earth twice in
one day?
First, let's convert the angular velocity to rad/s and then, we need to get the radius.
2rev / 24hours = 2.315e-5rev/s = 1.454e-4rad/s
To get the radius, we are going to combine two different equations. The standard FG equation
and FG = m * a. Watch carefully.
FG = (g * 5.98e24m * m2) / r2
FG = m * 9.8m/s2
(g * 5.98e24m * m2) / r2 = m * 9.8m/s2
The masses two unidentified masses cancel each other out leaving us with:
(g * 5.98e24m) / r2 = 9.8m/s2
r2 = 4.072e13m2
r = 6380941.665m
Now that we have those two components, we can calculate the centripetal acceleration.
aC = (1.454e-4rad/s)2 * 6380941.65m
aC = 0.135m/s2
The next lesson will work an example that encompasses many things
that we have learned thus far.
