In thinking back to the last module, you may have noticed that the amount of force required for
your leg muscles depended on where you placed the mass on your leg. The further a mass is
from a rotational pivot, the more force is required to rotate that mass. The center of mass has
changed, and as such, the rotation will be different. It is imperative for athletes to understand
the basics of center of mass. If they did not, they would be off balance during a performance
and this could lead to serious injury! Additionally, working on mechanical devices requires a
thorough understanding of torque. Imagine trying to change a flat tire with nothing but a tiny
pair of pliers. You would not be able to generate enough torque to turn the wheel nut!
Activity #2: Velocity of Center of Mass
Open Tracker and download the video from the lab 05 folder entitled “Pucks Collide”. We will
use this demonstration video to gain some sophistication in the Tracker software and illustrate
the motion of the center of mass.
a. Once you have the video open, be sure to set your scale and axes of the origin.
b. Now, click on the create button at the top and first choose “center of mass”. Then you
will click on the create button and choose “point mass” as in the past. You should see a
warning similar to the one below.
c. Choose, “Yes” to add mass A to the center of mass A.
d. Proceed to “shift+click” through the series of frames for puck A (green puck) using the
center of the puck as the place to click.
e. Repeat this procedure (b-d) for mass B, the red puck.
f. Once you have gone through each frame for each puck, you will see the position
marks for pucks A and B.
g. Then choose the masses for the pucks in the upper left corner to be 48, as the text in
the video suggests. You should then see a new track running through the middle of the
final frame, which indicates the position of the center of mass.
h. Now you can click on the acceleration vectors on the top right side of the video and
you now see tiny acceleration arrows indicating how the pucks accelerated in each
i. Lastly, you can click on the “multiply vectors by mass” button to change the
acceleration vectors into force vectors. Your final screen should look something like this:
This is a very messy screen, but keep in mind that the video is recording very fast, so there are
many frames on which to click. This means many arrow pointing in similar directions. One can
easily delete points by right clicking (control+click) on a point and select “Delete Selected Step”
to clean up the vectors.
3. Upload a snapshot of your final scene showing some vectors, the motion of the center of
4. Now click on the plot on the upper right side of the Tracker software and change the variable
to “cm A”, if it is not already. Notice that if you plot the motion of the center of mass in both the
x and y directions, you get a straight line! Why do you think that is? Both pucks took a curved
path, but is seems the center of mass was plodding along and never notice the collision. Can
you think of a reason why the center of mass speed would not change throughout the entire
collision? Respond using the physics terminology you have learned thus far in the course.
Do not worry if you have trouble answering #4. The concept of momentum is discussed in more
detail in the next segment, but hopefully in practicing with the Tracker software, you will keep
this video in mind as we discuss conservation laws next module.
Activity #3: Torque
We have explored the concept of center of mass a bit, but now it’s time to apply it coupled with
the concept of torque. As illustrated in lectures and textbook, any unbalanced torque will create
rotation. However, that implies that BALANCED torques will keep a rigid body stationary, or as
we say in physics, the object is in static equilibrium. There is no translation, nor rotation.
5. Describe a situation in your daily life, where something BIG is static equilibrium. Describe
what would happen if the BIG object were not in static equilibrium.
6. Now take a ruler or meter stick and “balance” it on your finger. You should do this in such a
way that ruler or meter stick does not rotate on any axis. Take a photo or sketch the “balanced”
stick in the space below. Describe how you placed your finger to get it to balance best. Also
describe any failed attempts at balancing it, which caused the stick to fall off your finger
7. Measure the mass of your stick with a kitchen scale, or a grocery store scale, and write it
here. Note, you should convert to kilograms for your final answer.
8. Assuming that the mass of your stick is PERFECTLY distributed, how much mass is on
either side of your finger? Include a justification for your estimate.
9. From the photo or sketch in #6, draw a force diagram notating all forces involved in
balancing the stick. Include distances to the force vectors from the finger, in your diagram.
10. Write out Newton’s Second Law of Rotational Motion for the diagram in #9. There is no
need to solve for anything, simply write it out in symbolic form.
11. Now you will have to use some sound judgement, as each experiment will be slightly
different for each student. You should place some mass that is roughly 10%-20% of the mass
of the stick, on the zero end of your ruler/meter stick. There is no need to be terribly precise in
how much mass you add, just try to estimate the added mass given your answer in #7. You
should attach the mass such that the masses do not fall off, by using some tape. These
masses could be a few paperclips for a small ruler, or a few pens or pencils for a larger meter
stick. Now balance the stick on your finger as you did in #6, only now you will likely have one
difference, the position of the finger! Take a photo or make a sketch of the balanced stick and
notate the position of your finger in the space below.
12. From your photo or sketch, draw a force diagram including distances to the forces from
13. Estimate how much mass of the ruler is on either side of your finger, and the position of the
center of mass portion of the ruler on the left and right side of your finger. You should have two
center of mass positions from this estimate; one left of the finger, and one right of the finger.
Write your estimates for positions and masses below.
14. Using Newton’s Second Law of Rotational Motion, write out the equation for the diagram in
#12. Note that you can place actual numbers in for the left and right center of masses of the
stick, the mass stick on the left and right of your finger. Lastly, you know that the position of the
added mass is on the end of the stick. Using these values, solve for the mass you added on the
end of the stick.
15. Using your kitchen scale, a grocery scale, or google, estimate the mass of the objects you
used and compare this to the calculated mass in #14. Find the percent difference and explain
the difference in terms of the physics learned in this lab.
16. Looking back at your answer to #5, comment on the following items:
A. Does your example in #5 truly exemplify static equilibrium?
B. Do Newton’s Laws of Rotational Motion directly apply to your example?
C. What do you think would happen if the object were not in static equilibrium?
D. Try to find a video online, of such a situation, where the object you have mentioned is
not in static equilibrium, and copy the link to the video in the space below your answer.
Now that you have had some practice with rotational motion, torque, moment of inertia, center
of mass, and the like you may want to include some of these concepts in your own lab video
These solutions may offer step-by-step problem-solving explanations or good writing examples that include modern styles of formatting and construction
of bibliographies out of text citations and references. Students may use these solutions for personal skill-building and practice.
Unethical use is strictly forbidden.
4. According to the principle of conservation of momentum, for an isolated system with no external forces, the initial total momentum of objects before a collision equals the final total momentum of the objects after the collision. Since the masses of two bodies are the same, the center of mass of the system should follow a straight line.
5. A Cable bridge
If the bridge is not in equilibrium then the structure will tend to oscillate and under large oscillations, bridge can be damaged...