Calculate the acceleration of rolling objects down an incline using their mass moment of inertia.
Race Parameters
°
Calculation Results
Enter incline angle
About this calculator
Quick Reference
I / mR²Moment of Inertia Factor
Solid Cylinder0.5
Solid Sphere0.4
Thin Hoop1.0
Overview
In a race down an incline, the object's acceleration depends on its mass distribution (moment of inertia) rather than its total mass. Objects with more mass concentrated near the center accelerate faster.
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Pro Tips
Acceleration = (g · sinθ) / (1 + I / (m·R²)).
Notice that mass (m) and radius (R) usually cancel out for standard shapes!
A solid sphere will always beat a solid cylinder.
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Fun Facts
"A solid cylinder (like a full toilet paper roll) accelerates at 2/3 the rate of a sliding object."
"A hollow hoop is the slowest common shape because its mass is furthest from the center."
"In a vacuum, all solid spheres of the same material color and density will tie, regardless of size."
