Rotational Inertia Equations

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Last updated 3:09 PM on 5/2/26
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8 Terms

1
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Parallel Axis Theorem

I_new = I_cm + Md²
- I_cm: rotational inertia when the the rotational axis 1) passes center-of-mass and 2) is parallel to the new axis in I_new (e.g. both point in x direction)
- d: perpendicular distance from the cm axis to the new, parallel axis of rotation

2
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Point Mass

I = mr²

3
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Hoop / Ring

I = mR²

4
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Solid Disk / Cylinder

I = ½ mR²

5
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Thin Rod about Center

I = 1/12 mL²

6
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Thin Rod about End

I = 1/3 mL²

7
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Solid Sphere

I = 2/5 mR²

8
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Hollow Sphere / Shell

I = 2/3 mR²