Download your PDF
Rolling Cylinder Ramp Race Calculator result sheet — free, supported by sponsors. Your download button appears in 20 seconds.
This free download is supported by sponsors — continuing in
20
Your file is generated in your browser when you choose Download — nothing is uploaded. If this calculator returns enough numeric data, the export also includes its best-fit chart alongside the readable table.
WorldCalculate result export
Rolling Cylinder Ramp Race Calculator — result sheet
Compare the ideal acceleration, final speed, and travel time of a solid cylinder, cylindrical tube, or thin shell rolling down a ramp from rest.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: For rolling without slipping, I is ½mR² for a solid cylinder, ½m(R²+r²) for a cylindrical tube, and mR² for a thin shell; ramp angle θ = asin(height/length); acceleration a = g sinθ ÷ [1 + I/(mR²)]; final speed v = √(2aL); time t = √(2L/a).
The race model isolates how mass distribution changes rolling motion on the same incline. It calculates the shape-specific axial moment of inertia, then uses a constant-acceleration, no-slip model to estimate the speed and time over the ramp length. Mass cancels from the ideal acceleration when the shape and radii are fixed, but it remains an input so the reported inertia and energy scale stay physically readable.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Rolling shape — 3 choices
- Mass — kg; minimum 1.0E-6; maximum 1000000000
- Inner radius — m; minimum 0; maximum 1000000
- Outer radius — m; minimum 1.0E-6; maximum 1000000
- Ramp vertical drop — m; minimum 1.0E-6; maximum 1000000
- Ramp length — m; minimum 1.0E-6; maximum 1000000
- Gravitational acceleration — m/s²; minimum 1.0E-6; maximum 100
Worked example
| Input | Value |
|---|---|
| Rolling shape | solid-cylinder |
| Mass | 1 |
| Inner radius | 0 |
| Outer radius | 0.06 |
| Ramp vertical drop | 1 |
| Ramp length | 4 |
| Gravitational acceleration | 9.80665 |
The ideal solid-cylinder model has I = 0.0018 kg·m², acceleration about 1.63 m/s², final speed about 3.62 m/s, and travel time about 2.21 s.
Assumptions and limits
- The object is a rigid, coaxial cylinder that starts from rest and rolls without slipping on a straight ramp with constant angle.
- The solid-cylinder option uses the outer radius as its radius and treats the inner-radius field as unused; the tube option requires inner radius smaller than outer radius; the thin-shell option concentrates mass at the outer radius.
- The ramp height is positive and smaller than ramp length, so the angle is defined by the entered geometry.
- Static friction is assumed sufficient for rolling and no rolling resistance, air drag, deformation, bearing friction, or ramp roughness is subtracted.
- The final speed follows energy-equivalent constant acceleration along the ramp; it is not a prediction for a real paper roll, bottle, or toy under every surface condition.
- Use a safe, controlled demonstration setup and keep the result separate from material strength, collision, or equipment decisions.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
No saved result was found. Please run the calculation first, then choose Download again.