Precision Heavy Steel Flywheel and Axle Drum
A massive, dynamically balanced 4.000 kg steel disk mounted on a precision horizontal axle with a concentric 20.0 mm radius cord drum.
Physics / Flywheel moment of inertia and rotational dynamics
FREE TO EXPLOREEXPERIMENT 23 · PHYSICS LABORATORY
Uniformly accelerated angular motion and determination of flywheel moment of inertia
Investigate the fundamental dynamic relation between applied net torque τ, moment of inertia I, and angular acceleration α for a precision heavy flywheel mounted on low-friction bearings, verifying the rotational analogue of Newton's second law α = τ / I across varying applied torques, and extracting the flywheel's moment of inertia from the inverse slope of the angular acceleration versus torque graph. Explore a virtual apparatus, collect readings and analyse a graph.
CHANGE · OBSERVE · MEASURE
Your virtual workbench.
ANGULAR ACCELERATION Α—
MEASUREMENT STATUS
Ready for a virtual observation.
Adjust the apparatus, then take a reading.
Readings are generated by an ideal model. The diagram is schematic and is not to scale.
Simulation assumptions and limits
This virtual experiment assumes a perfectly rigid, symmetric flywheel with zero bearing friction, zero aerodynamic windage, and an inextensible cord of negligible mass. It neglects the minor equivalent inertia m r² of the falling weight and assuming an exact single-layer winding. Generated readings reflect ideal Newtonian rotational dynamics; physical experiments will exhibit small random variations from bearing friction fluctuations. Theoretical angular acceleration: α = τ / I. Linearized relation: α = (1 / I) · τ. The ordinary least-squares regression extracts the slope S = 1 / I, from which moment of inertia is recovered as I = 1 / S. Reference flywheel moment of inertia I = 0.0500 kg m².
Know your apparatus.
Low-Friction Precision Ball Bearings and Rigid Wall Mount
Rigid cast-iron bearing housings supporting the flywheel axle with deep-groove miniature ball bearings to minimize rotational friction.
High-Resolution Optical Rotary Encoder and Digital Tachometer
An optical encoder disc with 360 pulses per revolution, coupled to a digital microprocessor counter measuring angular velocity and acceleration.
Calibrated Slotted Weight Set, Tow Cord, and Impact Cushion
Precision brass weights suspended by an inextensible monofilament cord wrapped around the drum, landing on a resilient energy-absorbing foam pad.
FOLLOW THE METHOD
A reason behind every step.
Investigate the fundamental dynamic relation between applied net torque τ, moment of inertia I, and angular acceleration α for a precision heavy flywheel mounted on low-friction bearings, verifying the rotational analogue of Newton's second law α = τ / I across varying applied torques, and extracting the flywheel's moment of inertia from the inverse slope of the angular acceleration versus torque graph. Suggested independent settings: 0.03, 0.06, 0.09, 0.12, 0.15 N m.
Bearing Inspection, Axle Metrology, and Zero Leveling
Inspect the flywheel mounting bracket with a spirit level to verify horizontal alignment of the axle. Measure the diameter of the axle drum at three orthogonal orientations using Vernier calipers, and calculate the mean drum radius r = 0.0200 m (20.0 mm). Give the unweighted wheel a gentle spin to confirm smooth, silent rotation.
Why this step matters
Accurate drum radius r is required to convert cord tension into applied torque τ = T · r, and bearing smoothness ensures minimal parasitic friction.
Static Flywheel Mass and Geometric Dimension Metrology
Record the manufacturer's certified mass of the flywheel disk M = 4.000 kg, or weigh the disk on a heavy-duty platform balance. Measure the outer radius R = 0.1581 m using an engineering steel rule. Compute the theoretical geometric moment of inertia I_geom = 1/2 M R² = 0.0500 kg m².
Why this step matters
Direct geometric metrology provides an independent theoretical reference standard against which the dynamic experimental result is compared.
Cord Attachment and Axle Drum Winding
Attach a loop at the end of the monofilament cord to the small driving peg on the axle drum. Wind the cord evenly in a single layer along the drum without overlapping turns. Suspend the initial hanging mass corresponding to an applied torque of τ = 0.030 N m (hanging mass m ≈ 153.0 g).
Why this step matters
Overlapping cord turns would increase the effective winding radius, systematically altering the applied torque during unwinding.
Release Execution and Angular Acceleration Measurement
Hold the flywheel at rest and zero the digital rotary encoder display. Release the wheel smoothly, allowing the weight to descend. The falling weight accelerates the wheel until the cord unhooks automatically from the peg at the floor. Record the constant angular acceleration α displayed on the digital tachometer to 0.001 rad s⁻².
Why this step matters
Allowing the cord to detach cleanly at the bottom prevents reverse winding, ensuring the recorded acceleration reflects purely forward accelerating torque.
Systematic Torque Sweep Across Five Load Stations
Repeat the winding, release, and timing procedure for applied torques of 0.060 N m, 0.090 N m, 0.120 N m, and 0.150 N m by adjusting the slotted mass suspended from the cord. Perform three successive trials at each torque setting to confirm repeatability.
Why this step matters
A five-point systematic sweep across a five-fold torque range establishes linearity and provides sufficient degrees of freedom for robust regression.
Coordinate Transformation, Regression, and Inertia Extraction
Plot angular acceleration α on the vertical axis against applied torque τ on the horizontal axis. Perform an ordinary least-squares linear fit to evaluate the slope S = 1 / I. Compute the experimental moment of inertia as I = 1 / S, evaluate statistical uncertainty, and compare with the geometric value.
Why this step matters
Ordinary least squares over the linear dynamic equation filters random timing noise and yields an unbiased dynamic measurement of moment of inertia.
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
α = (1 / I) · τ ⇔ I = 1 / S
| # | Applied torque τ (N m) | Angular acceleration α (rad s⁻²) | Applied torque τ (N m) | Angular acceleration α (rad s⁻²) | Remove |
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