What is moment of inertia?

Moment of inertia measures an object's resistance to rotational acceleration—the rotational equivalent of mass. It depends on both the total mass and how that mass is distributed relative to the rotation axis. Mass farther from the axis contributes more to the moment of inertia.

How do I calculate moment of inertia?

For a point mass: I = mr² (mass × distance squared). For common shapes, use standard formulas: solid cylinder I = ½mr², hollow cylinder I = mr², solid sphere I = ⅖mr², rod about center I = (1/12)mL². For complex shapes, add individual components or use integration.

Why does a figure skater spin faster with arms pulled in?

Angular momentum (L = Iω) is conserved. When the skater pulls arms in, moment of inertia (I) decreases because mass moves closer to the rotation axis. Since L must stay constant, angular velocity (ω) must increase. Less I means faster spinning.

What's the difference between moment of inertia and mass?

Mass measures resistance to linear acceleration (F = ma). Moment of inertia measures resistance to angular acceleration (τ = Iα). Two objects with the same mass can have different moments of inertia depending on shape and rotation axis. A long thin rod is harder to spin than a compact ball of equal mass.

How does moment of inertia affect motor selection?

Motors must overcome load inertia to achieve desired acceleration. Higher load inertia requires more torque for the same acceleration (τ = Iα). Motor inertia should typically be matched to or somewhat smaller than load inertia for optimal control. Mismatched inertia ratios cause control problems.

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About Moment of Inertia Conversion

Moment of inertia (also called rotational inertia or second moment of mass) quantifies an object's resistance to changes in rotational motion—the rotational equivalent of mass. Just as mass determines how hard it is to accelerate an object linearly (F=ma), moment of inertia determines how hard it is to accelerate rotation (τ=Iα). It depends on both total mass and how that mass is distributed relative to the axis of rotation—mass farther from the axis contributes disproportionately more.

The SI unit is kilogram square meter (kg·m²). Moment of inertia is fundamental to mechanical engineering, robotics, vehicle dynamics, flywheel energy storage, gyroscope design, and any application involving rotation. Engineers must calculate moment of inertia to size motors, design crankshafts, balance rotating equipment, and understand how systems respond to torques. The same mass arranged differently can have vastly different moments of inertia.

Our converter handles all standard moment of inertia units for engineering and physics applications, from precision servo motors to industrial machinery.

Common Moment of Inertia Conversions

From	To	Multiply By
kg·m²	g·cm²	10,000,000 (10⁷)
g·cm²	kg·m²	0.0000001 (10⁻⁷)
kg·m²	lb·ft²	23.73
lb·ft²	kg·m²	0.04214
kg·m²	lb·in²	3417
lb·in²	kg·m²	0.000293
kg·m²	oz·in²	54,675
oz·in²	kg·m²	0.0000183
lb·ft²	lb·in²	144
slug·ft²	kg·m²	1.3558

Moment of Inertia Unit Reference

Kilogram square meter (kg·m²) – The SI unit for moment of inertia. Used in physics and engineering calculations worldwide. Works directly with SI torque (N·m) and angular acceleration (rad/s²) in the rotational equation τ = Iα. A typical car wheel assembly has I ≈ 1 kg·m²; a figure skater with arms out ≈ 3-5 kg·m².

Gram square centimeter (g·cm²) – CGS unit, common for small objects and laboratory measurements. 1 kg·m² = 10⁷ g·cm². Useful for measuring small components like gears, pulleys, and precision mechanisms. Often used in physics education.

Pound square foot (lb·ft²) – US customary unit for larger objects. Common in automotive and aerospace engineering in the US. Vehicle driveline components and aircraft propellers are often specified in lb·ft². Requires care with units in calculations.

Pound square inch (lb·in²) – Used for smaller components, motors, and precision engineering. 1 lb·ft² = 144 lb·in². Common in servo motor and stepper motor specifications where loads are relatively small.

Ounce square inch (oz·in²) – Used for small motors, servo specifications, and precision instruments. Popular in hobby robotics and RC applications where components are small. 1 lb·in² = 16 oz·in².

Slug square foot (slug·ft²) – US engineering unit using slugs (1 slug = 1 lb·s²/ft ≈ 14.59 kg). Directly compatible with pounds-force and ft/s² in F = ma form, avoiding the mass/force confusion that plagues lb-based units.