Source: https://guthlabs.ai/docs/instruments/rolling-without-slipping-solver/
instrument / verified-clean
# Rolling Without Slipping Solver
The current ledger marks this instrument verified clean within the source-bound verification corpus.
Status: **VERIFIED_CLEAN**Lifecycle: **verified-clean**
## Inspectable records
[01**Overview**Purpose and lifecycle]()[02**Mechanism**Method and assumptions]()[03**Implementation**Binding and validation]()[04**Qualification**Evidence and errata]()
## Ledger state
The current ledger marks this instrument verified clean within the source-bound verification corpus.
**Area**: Physics — Kinematics/Projectiles/Orbits, Forces/Energy/Momentum, Rotational Dynamics, Gravitation, Oscillations/Waves, Optics, E&M Fields, Relativity, Quantum, Statistical Thermo
**Tranche**: tranche-6
**Evidence ID**: t6-037
**Ledger rows**: 1
No ledger note is attached.
## Review findings
The acceleration algorithm is a direct lookup-table evaluation, not an iterative method. The core acceleration formula is standard, but the instrument needs explicit angle units, an unambiguous cylinder definition, and additional inputs/formulas for velocity and race results. The honest-label warning about idealized no-slip and no rolling resistance is appropriate but should also state that sufficient static friction is assumed.
### Formula and scope findings
- The acceleration formula a=g sin(theta)/(1+I/(mR^2)) is correct for a rigid body rolling down a straight incline without slipping, assuming gravity is uniform and the object starts with no dependence on translational initial velocity.
- The stated solid-sphere example is correct: I/(mR^2)=2/5, so a=g sin(theta)/(1+2/5)=(5/7)g sin(theta).
- Velocity is claimed as an output, but no ramp length, elapsed time, initial velocity, or velocity formula is specified. For release from rest over distance s, the required formula is v=sqrt(2as); after time t, v=at.
- The shape lookup is ambiguous for cylinder: a solid cylinder or disk has I/(mR^2)=1/2, while a hollow cylinder has a different ratio. The catalog must explicitly define which cylinder is intended.
- The no-slip condition is not merely a label: static friction must be sufficient. For a body with k=I/(mR^2), the required condition is mu_s >= k tan(theta)/(1+k).
### Unit assumptions
- Use g=9.80665 m/s^2 unless a configurable value is explicitly provided.
- Angles are interpreted as degrees in these vectors and converted before applying sine: theta_rad=theta_deg*pi/180. The specification does not state whether the UI accepts degrees or radians.
- I/(mR^2) is dimensionless; acceleration is reported in m/s^2.
- For velocity checks, ramp length is in meters, initial velocity is in m/s, and the object is released from rest unless otherwise stated.
- The tested cylinder is explicitly treated as a solid cylinder, equivalent to a solid disk, with I/(mR^2)=1/2.
## Boundary hardening
**BREAK_CLAIMED** · SELF_FLAGGED
The specification defines only four recognized shapes and gives no behavior for an unrecognized shape. Without explicit validation, an unknown shape produces an undefined inertia-ratio lookup and therefore an undefined acceleration; the solver must reject it.
## Errata and corrections
No applied erratum is attached to this unique-name record.
## Inspectable example
4 review vectors are recorded. One source-bound sample is shown below.
````
{
"inputs": {
"shape": "solid sphere",
"angle": 30,
"angle_unit": "degrees",
"g": 9.80665
},
"expected_outputs": {
"acceleration_m_per_s2": 3.502375
},
"working": "k=I/(mR^2)=2/5=0.4. Convert angle: sin(30 degrees)=0.5. Denominator=1+0.4=1.4. Numerator=g sin(theta)=9.80665*0.5=4.903325. Therefore a=4.903325/1.4=3.502375 m/s^2."
}
````
## Related workflows
No source-defined multi-instrument workflow membership is recorded.
## Sources and evidence
These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.
- `VERIFIED_LEDGER.json · VERIFIED_CLEAN`
- `evidence-tranche6/tranche6-results.json`
- `BOUNDARY_HAZARD_CATALOG.json`