Toilet Paper Race Mass Moment of Inertia Calculator
Free calculate mass moment of inertia for rolling cylindrical objects like toilet paper rolls. determine moment of inertia using mass, radius, and calculate rolling motion for the classic toilet paper race experiment.
Input Parameters
Leave as 0 for solid cylinder
Results
Enter parameters to calculate moment of inertia
Mass Moment of Inertia Formulas
Solid Cylinder
I = ½mR²
About central axis
Hollow Cylinder
I = ½m(R² + r²)
Where r = inner radius
Toilet Paper Race
In a race down an incline, objects with lower moment of inertia accelerate faster. The moment of inertia affects how quickly the object can start rolling.
Rolling Motion
a = g sin(θ) / (1 + I/mR²)
Acceleration down incline