LIVEI = Icm + Md² · 0.50 + 2.00 = 2.50 kg·m²

3D Parallel-Axis Theorem

Shift the axis · reveal added rotational inertia

Teacher mode

Mission: move the axis

Shift the axle away from the center of mass and watch rotational inertia grow with distance squared.

Rigid bodyVisual mode

Mass2.0 kg

Radius / length1.0 m

Axis offset d1.0 m

Angular speed2.0 rad/s

Simulation speed1×

I = Icm + Md²
2.50 = 0.50 + 2.00 kg·m²

0.50Icm (kg·m²)

2.00Md² (kg·m²)

2.50Shifted I

5.00Rotational energy (J)

The active axle is parallel to the center-of-mass axis and separated by distance d.

Zoom1.0×

Step 1 of 100%

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LanguageNarrator

Narration speed1.0×

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What to watch

Watch the rotation axis slide away from the center of mass while staying parallel.

Parallel-axis theorem: I = Icm + Md².

Rotational energy: K = ½Iω².

Angular acceleration: α = τ ÷ I.

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