### Circular Motion Lab

Background:

Our goal for this lab is to determine an expression for a new (to you), non-linear type of acceleration, known as centripetal (or radial) acceleration.  Recall from the kinematics unit that there are three ways an object can change its velocity- it can speed up, slow down and (since velocity is a vector) change direction.  Until now we have only dealt with the speeding up and slowing down portions.  It is time to deal with the direction change.

Acceleration is also a vector quantity.  In linear motion, we have indicated the direction of acceleration by making it positive or negative.  In Uniform Circular Motion, our new unit, we can also use sign to indicate direction, however the sign refers not to left/right/up/down, but rather direction toward a certain the portion of a circle.  The convention we will use is: vectors pointing to the center of a circle are positive, vectors pointing radially outward from the center will be negative.

The word "centripetal" in centripetal acceleration means "center-seeking."  It is not immediately obvious that an object moving on a circular path has a velocity change directed inward, but hopefully the following graphic will make it a little more clear: The blue arrow shows the direction of velocity change from v​1​ to v​2​, and this change is directed inward.  Therefore, you could be going around a turn in a car at a steady 30 mi/hr, but you still have an acceleration directed toward the center of your circular path.

Goal:

You are to derive an expression (equation) for the acceleration of an object moving in uniform circular motion.

Strategy:

There are three variables that could potentially affect the acceleration of the object- mass, velocity and radius.  You are going to use a simulation (Gizmo) to alter these variables, one at a time, to see how they affect acceleration.  You will alter them using the slider controls on the Gizmo, shown below: The centripetal acceleration is represented by the blue arrow on the simulation, and the magnitude of this acceleration is found using the value of the first bar on the bar graph.  (You have to choose the acceleration graph, and click on "show numerical values.")

It is up to you how many times you change each variable and record the resulting acceleration.  As always, more data = prettier graphs, but since this a simulation, the numbers will be fairly perfect, and a ton of data will not be needed.

Make sure you control everything but what you are testing at the moment.  Record the values of the controls (ex:  I could vary the radius while keeping the mass at 6.2 kg and velocity at 9.1 m/s.)

Record your data in three separate tables (one for each new independent variable.)  Create three graphs, as follows:
• Radius on x, acceleration on y
• Mass on x, acceleration on y
• Velocity on x, acceleration on y

Two of these will result in curves that need to be linearized.  Refer to your summer assignment for the linearization strategy.  Each linear graph should be accompanied by the equation for the line, written in a general form (replace y, m, x, b with either words, variables, or "k" representing a constant, the meaning of which is not yet known.)

Your final task will be to put the pieces together to form a logical equation for centripetal acceleration.  Not every variable (of radius, mass, velocity) must be in your final equation.  The biggest clue for forming this equation is the value and units for your constant (k) in each graph equation.

Recall that you have previously created an account on explorelearning.com and were to retain your login information.  Here are the class codes that were given previously, in case they are required again:

Pd 1: M5DNQUQLYG   Pd 2: RHCCDP29CG Pd 6: L8CPLDDHKZ   Pd 7: FE5P47LNWC