Parallel Axis Theorem
Relates moment of inertia about any axis to the moment of inertia about a parallel axis through the center of mass.
Variables
Derivation
Expanding I = ∫(r + d)²dm and using the definition of center of mass gives I = I_cm + Md².
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- Icm = 2 kg·m² (Moment of inertia (CM))
- M = 3 kg (Mass)
- d = 4 m (Distance)
Result: I = 50 kg·m²
Other mechanics formulas with the same quantities
- Moment of Inertia (Solid Sphere) (Rotational Motion) shares Moment of inertia, Mass
- Newton's Second Law (Rotation) (Rotational Motion) shares Moment of inertia
- Rotational Kinetic Energy (Rotational Motion) shares Moment of inertia
- Angular Momentum (Rotational Motion) shares Moment of inertia
- Rolling Kinetic Energy (Rotational Motion) shares Moment of inertia
Where this formula is listed
- Mechanics formulas, under Rotational Motion, alongside Angular Velocity, Angular Acceleration, Linear-Angular Velocity Relation, Centripetal Acceleration and Centripetal Force.
- In the mechanics list it comes after Moment of Inertia (Rod, Center) and before Rolling Kinetic Energy.
- Mechanics formula sheet, one of 58 formulas printed with symbol keys and SI units.
- The full formula index, grouped by category and topic.
Common questions
What is the Parallel Axis Theorem formula?
Parallel Axis Theorem is written I = I_cm + Md². Relates moment of inertia about any axis to the moment of inertia about a parallel axis through the center of mass. It belongs to Mechanics, under Rotational Motion.
What are the units in I = I_cm + Md²?
In SI units, I is moment of inertia, measured in kg·m²; I_c m is moment of inertia (cm), measured in kg·m²; M is mass, measured in kg; d is distance, measured in m.
How is the Parallel Axis Theorem formula derived?
Expanding I = ∫(r + d)²dm and using the definition of center of mass gives I = I_cm + Md². The result is I = I_cm + Md².