Teach lesson
Moment of inertia: the same masses, near or far from the axis?
Students use two controlled runs of the Moment of Inertia remote lab to test how moving the same masses changes rotational response.
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Learning Outcomes
Run a controlled comparison in which only the point-mass distance from the axis changes.
Extract peak velocity and elapsed time to peak from the laboratory spreadsheet.
Use I_total approximately equals I_bar plus 2mr squared to predict the effect of mass distribution.
Write an integrated explanation supported by a representative measured comparison.
Identify what the experiment cannot establish from its stored velocity-time recordings.
Student activity preview
Activity Content
Preview only. In a class session, students can fill in responses and submit their work to the teacher.
A rotating system with one important difference
7 min
On a spinning playground ride, two riders can sit near the centre or move towards the edge. The total mass has not changed, but will the ride respond in the same way when a force makes it turn?
You will investigate that question with a real remote apparatus. Both runs use the same bar, the same two point masses, and the same hanging mass. The only planned change is the distance of the two point masses from the rotation axis.
Real apparatus: masses near the axis
Real apparatus: masses far from the axis
The first photograph is the near setup and the second is the far setup. Both show the real apparatus, not a result. They use the same bar and masses; only the distance of those masses from the axis changes.
Moment of inertia, I, describes how strongly a rotating system resists a change in its rotational motion. For this comparison, an approximate model is:
Model for the bar and two equal point masses
I_{total} \approx I_{bar} + 2mr^2
Here m is the mass of each point mass and r is its distance from the axis. The same hanging mass provides a comparable driving effect in both runs.
According to the model, which setup has the larger contribution from the two point masses?
In one or two sentences, connect your choice to the system's expected response when the same hanging mass drives it.
Run the controlled near/far comparison
15 min
The interface may use English or Spanish labels. The choices you need are Bar / Barra, Point masses / Masas puntuales, Near the center / Cerca del centro, Far from the center / Lejos del centro, and Hanging mass 1 / Masa colgante 1.
Each configuration plays a stored recording from the real apparatus. Reopening it returns the same recording; it is not an independent repeat. Use the spreadsheet from each run. Its columns are Velocity vector (m/s) and Time (s). Because the graphs can use different vertical scales, compare the spreadsheet numbers, not their apparent heights.
Open the Moment of Inertia lab
Open the lab from this activity and choose Start configuring / Empezar a configurar.
Select Bar / Barra, then Point masses / Masas puntuales.
Select Near the center / Cerca del centro and Hanging mass 1 / Masa colgante 1.
Choose Start measurement / Comenzar medición. On the observation screen, press Start / Iniciar and wait for the recorded run to finish.
Choose Download spreadsheet / Descargar hoja de cálculo and keep the file open.
Return to Configuration / Configuración. Keep the bar, point masses, and hanging mass 1, but select Far from the center / Lejos del centro.
Play the recorded run to the end and download the second spreadsheet.
Return to this activity with both files open. Then mark the lab block complete.
Turn the two spreadsheets into evidence
9 min
Enter values from the two files, not values estimated from the visual height of the graphs. Keep three decimal places for velocity and two decimal places for time.
For each file, use this quick spreadsheet method:
1. In cell C1, outside the two data columns, enter =MAX(A:A) to obtain the greatest value in the velocity column.
2. Use Find to locate that value in column A, then read its time from column B in the same row.
3. Copy the first time in column B and calculate elapsed time to peak = peak time - first time.
Near/far measurements
Complete exactly the two starter rows. First time and peak time come directly from the spreadsheet; elapsed time to peak is their difference.
| Configuration | First time s | Peak velocity m/s | Time at peak s | Elapsed time to peak s |
|---|---|---|---|---|
Which statement matches the values in your completed table?
Explain what changed—and what the data do not prove
9 min
The lab information gives r = 0.0265 m for the near position and r = 0.170 m for the far position. Because the two point masses are unchanged, their mass cancels when their ideal contributions are compared:
Ratio to calculate
R=\left(\frac{0.170}{0.0265}\right)^2
Calculate R to the nearest whole number. R is the far-to-near ratio of only the ideal 2mr² point-mass contribution; it is not a measured-velocity ratio. In one sentence, explain why this model-term ratio need not match the change in reported velocity.
In 2–3 sentences, write one connected explanation of how moving the same masses farther from the axis changes moment of inertia and rotational response. Support your claim with one representative numerical comparison from your table—either the two peak velocities or the two elapsed times—and explain the direction using r². Use R only to compare the ideal 2mr² contribution of the two point masses; do not treat it as a measured-velocity ratio.
Which conclusion is beyond what this experiment can establish from these stored recordings?