Assignment 7: Circular Motion
Circular motion is an integral part of our
everyday lives. We experience circular
motion when we leave highways on cloverleaf exits and on amusement park
rides. Countless systems and devices
leverage circular motion. We will
discuss real-world applications in this module's discussion. In this lab, you will directly experiment
with uniform circular motion and quantify the behavior of a simple system. To execute the lab, you'll synthesize your
knowledge and experience with free-body diagrams and Newton's second law.
In this lab, you will create a simple
system of two different masses connected by a piece of fishing line. Here's the twist: The fishing line is
threaded through a tube. You will rotate
the tube and achieve an equilibrium situation where the lower mass is
vertically stationary. You will then use
your knowledge of circular motion to analyze the situation.
This activity is based on Lab 8 of the
eScience Lab kit.
notes as you perform the experiment and fill out the sections below. This document serves as your lab report. Please include detailed descriptions of your
experimental methods and observations.
sure you use fishing line instead of string for the experiment. Can you guess why?
careful when you rotate the mass. Be
aware of your surroundings so nothing is inadvertently hit by the rotating
the aid of a partner to time your experiments.
Material and Methods
for 15 revs
this column after performing the calculation in question 5 below.
on your results from the experiment, please answer the following questions:
- Draw a circle
to represent the path taken by your rotating mass. Place a dot on the
circle to represent your rotating washer. Add a straight line from the dot
to the center of the circle, representing the radius of rotation (the
string). Now label the direction of the tangential velocity and the
- Here is a
diagram of our experimental situation:
Please add vectors to create a
free-body diagram. Assume that m1 is rotating at a speed v with a constant radius R.
The following forces should be
included in your free-body diagram:
in the string
force on the rotating mass
force on the hanging mass
Hint: Each mass experiences
the tension in the string. The string
tension ultimately cancels out when you solve Newton's equations of motion for
3. From your free-body diagram, write the sum
of the forces experienced by mass m1. From your free-body diagram, write the
sum of the forces experienced by mass m2.
(For the equation for mass m1,
use the following relations to replace the speed, v: v = wR,
where R is the radius of rotation w
= 2p/T, where T is the period of rotation.)
In question 4 you will
solve the two above equations to obtain the period of the rotating system in
terms of the radius of rotation and the two masses, m1 and m2.
- Solve the
above equation for the period, T.
- Now let's
look at the special case of our experiment: 4m1 = m2. Show that our general expression for the
period T becomes:
Using this expression for the
period, fill in the theoretical period in the results table.
- How did the
period of rotation vary as you changed the radius? How does the angular
- Were your
experimental values close to the theoretical values? How could you improve
the experiment to reduce error?