Circular Motion

Jan Dudzik                     Whitney Young H.S.
                               211 S. Laflin
                               Chicago, Ill. 60607
                               (312) 534-7539

Objective:

Students will be able to recognize centripetal force and discern that radius, 
mass and period influence this force.

Apparatus: 

Group Pack: Centripetal Force Apparatus (Ball point pen tube, string, three 2-
holed rubber stopper, butterfly paper clip), 30 metal washers, timer, tape,
meter stick. 

To Assemble the Centripetal Force Apparatus:  Pull the 2 m. string through the 
empty pen tube until a little over a meter passes through the tube.  Next, 
attach the rubber stopper to one end of the string by pulling it about 15 cm. 
through one hole, back through the second and fastening the string to the part 
that enters the first hole.  Measure off 1 meter of the string that enters the 
first hole.  Take the other end of the string and attach a paper clip.  Measure 
off 1 meter of string on the apparatus starting from the rubber stopper and 
ending at the top of the tube that you slid up to the meter mark.  Place a piece
of tape securely on the string just underneath the other end of the tube.  Place
the apparatus in a ziplock bag carefully to avoid tangles. 

Strategy:

Divide the class into small groups.  Give each group a pack.  Show students how 
to get the centripetal force apparatus working by grabbing the pen tube with the
rubber stopper at the top with one hand and with the other hand, hold the paper 
clip tightly.  Hold the tube vertically above your head and get the stopper 
moving in a circle parallel to the floor.  Move your hand in smaller and smaller
circles until you can keep the ball going in circles by only moving your hand in
tiny circles.  Establish, through questions and class discussion, that the ball 
wants to travel in a straight line but it is being pulled back by the string.  
Illustrate this by letting go of the paper clip and have them observe.  Identify
this pull of the string on the stopper as a force towards the center or 
centripetal force.  Write the word and its definition on the board. 

Instruct students to explore this force by having one student in the group get 
the apparatus going and then pull the string and the paper clip with 10 washers 
on it down slowly to see what happens.  Ask each group to tell what they 
discovered.  Next, have students measure 30 cm. from the stopper to the top of 
the tube and then place a piece of tape just under the tube.  Have the twirler 
get the apparatus going and look straight ahead and count the number of times it
passes in front of him starting with zero up to 30, making sure to keep the tape
just under the tube at all times.  Have one student time the 30 revolutions.  
Have a recorder place the time on the board.  As a class, determine the average 
of all the times.  Instruct the students to repeat the above for 60 cm. and 90 
cm.  Calculate the period for each radius, using the average time in seconds and
dividing it by the number of revolutions.  Make a  class graph of Radius vs. T 
(period).  Summarize with the class that, from the data, the period has a direct 
relationship to the square of R, or as the radius increases, so does the period; 
and conversely, as the radius decreases, so does the period. 

Next, have students explore what happens to the period when mass increases.  
Have each group time 30 revolutions of 1 stopper with a 1 meter radius and a 
constant force of 10 washers.  Have each group place time on the board and take 
the average to calculate the period.  Repeat with 2 stoppers and with 3 
stoppers.  (Attach the stoppers to the first one with more string--be sure to 
remind students to keep the tape just below the tube.)  Plot as a class, mass 
versus T and summarize the relationship as the mass to the square of the period. 

Last, have the students explore what happens to the period when force increases
by adding washers to the clip in 5 washer intervals up to 30.  Have each group 
take a timing for each interval of 5 washers while keeping the radius at 1 meter
and the mass at 1 stopper and the tape just below the tube.  Find the average 
time.  Calculate the period for each 5 washer interval and use the data to plot 
class graph of Force vs. T (period).  Note that the graph reveals that F is 
inversely related to the square of the period or, as the force increases, the 
period decreases. 

Math: Go over the mathematical derivation of F = 4pi2Rm/T2

This will take at least 3 class periods.