University of Calgary
Department of Physics and Astronomy
PHYS 211/221, Fall 2022
Labatorial 4: Circular Motion
Overview:
In this lab you will explore the motion of a
puck on a frictionless air table as it undergoes
uniform circular motion. Two pucks are fitted
with central pegs and connected by a string:
the central puck is held in place while the
outer puck undergoes circular motion. Using
this setup, you will examine the relationships
between angular position, angular velocity,
tangential velocity, and period in uniform
circular motion.
This figure shows a motion diagram for a puck
undergoing circular motion. Is this uniform or
nonuniform circular motion?
Pre-Lab Reading:
Sections 4.4–4.6 of “Physics for Scientists and Engineers,” R.D. Knight, 4th Ed. Please
complete Checkpoint 1 (page 2-4) prior to the lab. Your TA will check if you have Checkpoint
1 filled-in and grant you entry to the lab based on that.
Equipment:
Air table, air supply, camera, camera mount stand, 2 large pucks, 2 central pegs, ImageJ
software, camera software, Excel, string (its length should be half width of the air table).
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PHYS 211/221, Labatorial 4, Fall 2022
1
Uniform Circular Motion
Earth is a planet that is approximately spherical and it rotates once on its axis every day.
What this implies is that objects that are fixed on Earth’s surface are undergoing circular
motion. The circular paths are given by the lines of latitude: objects on the equator follow
a circle with radius RE = 6371 km, while objects at the poles follow a circle of zero radius.
Calgary is on the 51st parallel, meaning that the angle it makes with Earth’s centre and a
point on the equator is θ = 51◦ , as shown in the diagram.
Question 1: What is the radius RC of our circular path here in Calgary?
Question 2: What is the relationship ω and the period T ?
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PHYS 211/221, Labatorial 4, Fall 2022
Question 3: What is the period T of this circular motion (measured in seconds)?
Question 4: What is the relationship between the angular position θ and the arclength
s; angular velocity ω and tangential velocity vt ; angular acceleration α and tangential
acceleration at ?
Question 5: Is the angular velocity of Calgary ωC greater than, equal to, or less than the
angular velocity of a point on the Equator ωE ? Why?
Question 6: Is the tangential velocity of Calgary vt,C greater than, equal to, or less than
the tangential velocity of a point on the Equator vt,E ? Why?
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PHYS 211/221, Labatorial 4, Fall 2022
Question 7: What is the centripetal acceleration ac of Calgary as Earth rotates on its axis?
Question 8: What is the angular acceleration α of Calgary as Earth rotates on its axis?
Question 9: Is the circular motion of Calgary as Earth rotates best described by uniform or
nonuniform circular motion? Why?
B:
A:
CHECKPOINT 1: Before moving on to the next part, discuss your
results as a group, then have your TA evaluate your answers.
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PHYS 211/221, Labatorial 4, Fall 2022
2
Recording a Video of Circular Motion
In this section you will record a video of a puck undergoing uniform circular motion. To
achieve this, you will use two pucks, each fitted with a central peg: with one finger, one of the
pucks will be held stationary in the centre of the table, while the other puck will be attached
to the first with a string and set to travel in a circular trajectory. When you are ready to
start taking your data, please follow these steps:
1. Turn on the air supply and place two small pucks on the air table.
2. Hold one puck in the centre of the table and set the other puck into circular motion.
3. Record the puck undergoing uniform circular motion for at least two full revolutions.
4. Follow the steps in “Recording and Analyzing Videos”. Begin cropping the video
after the puck has completed one full rotation and end it at one half or three quarters
of a rotation later.
5. Import your data into the Excel template “Lab 4 template (a)”.
6. In one of the video frames, select the coordinates of the centre of the central puck
(X0 , Y0 ) and input the values in the appropriate fields in the template.
Question 10: When you are processing the video, why do you need to pick the (x, y)
coordinates of the stationary central puck?
Question 11: When you pick the (x, y) coordinates of the stationary central puck, can you
use any point on the puck or does it have to be at the centre? Why?
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PHYS 211/221, Labatorial 4, Fall 2022
Question 12: Below is a figure showing the air table’s surface, along with the (X, Y )
coordinate system used by ImageJ. On the figure, draw the trajectory (including direction) of
your puck, indicate the location of the central puck, and draw an appropriate (x, y) coordinate
system. Where did you choose the origin and why?
Question 13: Do you expect the outer puck to experience a centripetal acceleration ac ?
Why or why not?
Question 14: Do you expect the outer puck to experience a tangential acceleration at ? Why
or why not?
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PHYS 211/221, Labatorial 4, Fall 2022
Question 15: Do you expect the outer puck to experience an angular acceleration α? Why
or why not?
Question 16: What is the difference between centripetal acceleration and tangential acceleration?
Question 17: In what direction does the centripetal acceleration point? Can it ever point
in the opposite direction? Why or why not?
B:
A:
CHECKPOINT 2: Before moving on to the next part, discuss your
results as a group, then have your TA evaluate your answers.
Question 18: Insert the appropriate columns from your data file into the Excel template.
Does your data describe uniform circular motion? Explain how you determined this.
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PHYS 211/221, Labatorial 4, Fall 2022
Question 19: Use the arrows in the motion diagram generated in the template to find the
direction of the acceleration vector ~a at three different points. Are your findings consistent
with uniform circular motion? Explain.
Question 20: How would the direction of the acceleration vector ~a change if you were
considering a case of nonuniform circular motion? Explain.
Question 21: For the case of nonuniform circular motion, what are the two types of
acceleration possible? In class there seem to be three types of acceleration present in circular
motion, but two of these are related. Which ones are related?
Question 22: For circular motion (both uniform and nonuniform), does the acceleration
vector ~a always point radially inward? Explain why, making explicit reference to the two
possible types of acceleration.
B:
A:
Last Checkpoint! Before being dismissed from the lab, discuss your
results as a group, then have your TA evaluate your answers. Be sure
to sign the grade sheet before you leave.
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