ONE FORMULA, ONE ANSWER
Rolling acceleration on an incline calculator
Compute down-slope acceleration while accounting for both translation and rotation. Choose input units and calculate one value within the stated conditions.
Inputs
Calculations run in this browser. Scientific notation such as 1.2e-3 is supported. Do not group thousands.
Result
Down-slope acceleration a
Enter values and select Calculate.
a = g sin θ / [1 + I/(m r²)]
Assumptions
Required: a rigid body, a uniform slope, 0 ≤ θ < 90°, and enough static friction for rolling without slip. I is about the rolling axis through the center of mass. Excluded: air drag, rolling resistance, and slipping.
Displayed values are floating-point approximations. Design safety factors and unprovided error contributions are not calculated.
Formula references and credits
NaNa Lab created the code, descriptions, icons and preview images. Text, figures and code from the linked references have not been reproduced.
Physical constants: NIST / CODATA 2022. The values of μ₀ and ε₀ are measured recommendations, not exact defining constants. Values and precision notes are in the source record.
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