Names: _______________ _______________ _______________ Section: ______
ROTATIONAL KINEMATICS
This workshop has three parts, all related to basic concepts of rotational motion.
1. First you will verify the relationship S = R between arc length S, angle  and radius R.
To do this you will measure arc length around a circular force table that has angle
graduations around the circumference. First measure the radius of the table: R =
________(cm). Use a piece of string to measure the arc length for the following angles
and fill in the table.
(degrees)
(radians)
S (cm)
S/R
30
90
225
Within the accuracy of the measurement, are the values of S/R in agreement with the values
of  ?
2. Now assume the force table is free to rotate about a vertical axis through the center of
the table. For each situation below indicate the direction of the angular velocity  and
of the angular acceleration. Use the notation: in = into the paper, out = out of the
paper, and 0 = zero magnitude. The curved arrows show the direction of rotation. Your
instructor will review these concepts before you attempt to answer.
Disk turning at constant
angular velocity in CCW
direction


Increasing angular
velocity in CCW
direction
Decreasing angular
velocity in CW
direction




3. Now you will examine the relation v=r for two flags of roughly equal width at two
different distances from the center of a rotating disk. You will measure v for each flag
by determining the time it takes for it to pass through a photogate. You will measure 
for each flag by measuring the time for it to make complete revolution. Each
measurement will be done twice.
Procedure
Position the two flags such that one flag (Outside) is at the edge of the disk, and the other
(Inside) is about halfway out to the edge. It is easier to measure the radii if the flags are
vertical. Measure the two radii and the two widths and record them below.
(O) r= ______(cm)
w= _______(cm)
(I) r= ______(cm)
w=________(cm)
Turn on a small stream of air to the disk on the air table and set the disk rotating at no
more than one revolution per second. Be sure that the flags pass easily through the
photogate. Start the LoggerPro program by opening the file for this lab. (Login as
"student",
and look under "Course Folders", "124", "lab 1 - rotational dynamics".)
Set the disk spinning, hit “Collect”, and let a few measurements accumulate in the table.
[The plot here is not relevant.] Collection should stop automatically when the table has
twelve numbers. The numbers are the times that an edge of a flag passes the photogate-first the leading edge and then the trailing edge of one flag, then the leading and then the
trailing edge of the second flag, and then the first flag on its second pass, and so on. Thus
the difference between the first two numbers is the time it take for the first flag to pass
through the gate and the difference between the next two numbers is the time it takes the
second flag to pass through the gate. The very first number is always zero and the fifth
number is the time for the first flag to make one revolution. Look carefully at the numbers
to see that they make sense to you. Observe that there are alternating short and long
durations: the shorter duration is from the flag at the larger radius.
Data
Once you understand the table of numbers, take another set of data and record all the
numbers here:
Pass 1
0.00
Pass 2
Pass 3
Now use these data to determine the quantities in the table below. The subscripts 1 and 2
refer to the first and second pass through the photogate. t is the length of time it takes a
flag to pass through the photogate.  is the time for one revolution.
Calculations
Flag O
t1 (s)
v1 (cm/s)=w/ t1
Flag I
 1(s)
1 (rad/s)=2/ 1
v1 / 1 (cm)
t2 (s)
v2 (cm/s)
2(s)
2 (rad/s)
v2 / (cm)
Are the values of  approximately the same for the two flags? Should they be?
Are the values of v approximately the same for the two flags? Should they be?
Do your results confirm the relation v=r? Explain.
What is the approximate value of the average angular acceleration ?