Rotational Dynamics (Energy)
By
Todd May
Lab Partners
Ryan Condon
Mike Moore
Mason O’Lennick
November 7, 2008
Physics 201
Lab Section 2
Introduction
In this lab we looked at rotational motion and more specifically the inertia of an object in
rotational motion. We calculated the moments of inertia of objects two very different ways and
compared them. One way we used the idea of energy conservation and derived an equation for
the moment of inertia in terms of other measurable quantities. The other way we measured the
speed of rotation and calculated it from that.
Materials
1 rotational motion sensor with interface cable
1 rotational motion equipment kit: bar with moveable masses
1 large ring stand with base
1 small hanging mass set
1 vernier calipers
Thread, scissors
Metric ruler
Procedure
In this lab we had a rotational motion kit which rotated two masses horizontally about a
vertical axis. To generate the rotational motion we had a thread wrapped around a pulley
attached to the axis and had a mass hanging on the other end. There was a pulley in the middle of
the thread to make it pull vertical to the rotational axis. The two masses slid onto a metal bar
which rotated and had a screw that we tightened to hold them in place.
Now for the first part of our experiment we measured the mass of our two masses, the
radius of the circle the masses rotated about, and the distance that the mass on the end of the
thread would fall before it ran out of thread. Then we calculated the inertia of the two masses and
added them together to get the total moment of inertia of our two masses. We also calculated the
error in the moment of inertia value.
For exercise two we used our rotational motion system. We hung a five gram mass on the
thread and let it fall, spinning the masses on the rod. The hanging mass was hanging over the
edge of the counter so it could fall farther than just the height of the stand. Then we measured the
change in angular velocity of our masses with our rotational sense hooked up to the computer.
Next we wound the thread back up, took the two masses off the bar, and let it go again while
measuring the change in angular velocity again. Now we had the angular velocity of the system
with and without the masses on the bar. Now from our data we had collected we were able to
find the moment of inertia of the two masses by deriving an equation from the fact that the
moment of inertia of the system with the masses on, minus the moment of inertia of the system
without the masses on gives us the moment of inertia of just the masses. We repeated exercise
two five more times, each time incrementing the hanging mass by five grams. On the last run we
had a total of 30 grams hanging from the thread. The angular velocity increased as the hanging
mass increased as one would expect. Then we found the average of the inertias and then found
the standard deviation of them. Then we compared that to the moment of inertia we had
calculated in exercise one. The difference of the two inertias was less than the error.
Now that we had all our data we wanted to find out how much effect friction had on our
experiment. To do this we created a graph with hanging mass on the y axis and 1/(2gh/ω22 2gh/ω12) on the x axis. This made the slop of the line equal to the moment of inertia of the two
masses we had on the rod. Then by looking at where the best fit line of these points crossed the y
axis we were able to determine how much of the hanging mass was eaten up by friction.
Measurements
All our measurements are recorded in the yellow cells of the attached excel table.
Equations
Equations shown on excel table.
Results
The moment of inertia we calculated for the runs in exercise two were very close but as
the hanging mass increased the inertia would constantly decrease. This could mean that the
heavier masses increased the frictional force the system experienced, but the frictional force was
still very small. Looking at the y intercept of the graph we created the masses used to overcome
friction was only 1/3 of a gram! Our system had very little friction which I expected after
watching how well the masses spun and how long they would keep going even with no forces
accelerating the.
Conclusion and Summary
When we compared our moment of inertias we found that they were the same. The
difference of the two numbers was less than the error associated with the difference. This shows
that there is more than one way of calculating the moment of inertia and they are both just as
good. They just use different information so depending on what information we know or can
obtain easily we can base our decision on which equation to use. This was another successful lab
where our numbers came out like we wanted them to and we did not have any big errors.