Uniform slender rod
Supply the rotating test body: mass M = 0.500 kg and rod length D = 0.500 m.
Physics / Bifilar suspension
FREE TO EXPLOREEXPERIMENT 03 · PHYSICS LABORATORY
Moment of inertia by bifilar suspension
Determine the moment of inertia of a uniform slender rod about its vertical centre-of-mass axis from bifilar oscillations at different string lengths. Explore a virtual apparatus, collect readings and analyse a graph.
CHANGE · OBSERVE · MEASURE
Your virtual workbench.
TIME FOR 20 OSCILLATIONS—
MEASUREMENT STATUS
Ready for a virtual observation.
Use ≤5° and keep amplitude fixed for a measurement series.
Adjust the apparatus, then take a reading.
Timing is generated from the model; a short on-screen trial represents a longer physical interval. Animation is illustrative.
Simulation assumptions and limits
The model assumes a rigid uniform slender rod, equal massless inextensible strings, symmetric attachment points, matching upper and lower separation, a horizontal equilibrium rod and small isolated torsional motion. It ignores string torsional stiffness, damping, attachment inertia, finite rod width, mode coupling and support movement. The reference g is 9.80665 m/s squared. Generated readings and accelerated animation cannot reproduce the alignment difficulties or measurement uncertainty of a physical suspension. A finite-width bar requires the appropriate inertia formula; the half-separation convention must be checked before comparing with any other apparatus. Equal, parallel strings are attached symmetrically about the centre of mass. The model uses the small-yaw relation T = 2π√[IL/(Mga²)]. It assumes negligible string mass, rod width, damping and support compliance. The simulated target inertia is Mℓ²/12. Angles above 5° cannot be recorded.
Know your apparatus.
Two strings and rigid overhead support
Suspend the rod horizontally using equal strings and matching top and bottom separation 2a = 0.200 m.
Rule and balance
Measure equilibrium string length L, half-separation a, rod length D, and rod mass M.
Timer and angular marker
Time 20 small torsional cycles using a consistent orientation and direction.
FOLLOW THE METHOD
A reason behind every step.
Determine the moment of inertia of a uniform slender rod about its vertical centre-of-mass axis from bifilar oscillations at different string lengths. Suggested independent settings: 0.3, 0.45, 0.6, 0.75, 0.9 m.
Record rod properties
Record M = 0.500 kg, D = 0.500 m and theoretical I = MD squared/12. Identify the vertical axis through the centre.
Why this step matters
The theoretical comparison must refer to the same axis as the motion.
Align the suspension
Set equal string lengths L. Keep the rod horizontal, with upper and lower attachment separations both 0.200 m and centred about the rod midpoint.
Why this step matters
This establishes equal parallel strings with a = 0.100 m, matching the formula.
Excite one small mode
Twist the rod only a few degrees about its central vertical axis and release without a push. Avoid lateral swinging and rocking.
Why this step matters
The small-angle theory assumes predominantly torsional motion.
Time 20 full oscillations
Start at a chosen orientation moving in one direction and stop after 20 returns in the same direction. Record the generated time; repeat if available.
Why this step matters
Using a fixed phase prevents half-cycle counting and spreads endpoint timing uncertainty over many cycles.
Vary string length
Use at least five well-spaced values of L while retaining the same rod and attachment spacing. Recheck equal lengths and horizontality each time; calculate T = mean time/20 and T squared.
Why this step matters
Only L should vary when measuring the T squared versus L relationship.
Fit and compare
Fit T squared = mL + b. Calculate I = mMga squared/(4pi squared), inspect intercept and residuals, and compare with 0.0104167 kg m squared with suitable uncertainty discussion.
Why this step matters
The gradient supplies the measured-model estimate; a comparison needs assumptions and uncertainty to be meaningful.
YOUR NOTEBOOK · 0 OBSERVATIONS
Turn measurements into a result.
Points are your observations. The fit uses SI x and y values before display scaling.
LINEAR FIT · y = mx + b
T² = mL + b; I = mMga²/(4π²)
| # | Suspension length L (m) | Time for 20 oscillations (s) | String length L (m) | Period squared T² (s²) | Remove |
|---|
No readings yet. Take a virtual measurement and record it.
Calculate it yourself.
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