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Mechanics
Mechanics

Moment of Inertia (Rod, Center)

I=112ML2I = \frac{1}{12}ML^2

Moment of inertia of a thin uniform rod rotating about its center, perpendicular to its length.

Variables

I
Moment of inertia
Rotational inertia
kg·m²
M
Mass
Total mass of rod
kg
L
Length
Length of rod
m

Derivation

I = ∫r²dm. For a rod: I = ∫₋L/2^L/2 x²(M/L)dx = (1/12)ML².

Your notes

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Common questions

What is the Moment of Inertia (Rod, Center) formula?

Moment of Inertia (Rod, Center) is written I = 1/12ML². Moment of inertia of a thin uniform rod rotating about its center, perpendicular to its length. It belongs to Mechanics, under Rotational Motion.

What are the units in I = 1/12ML²?

In SI units, I is moment of inertia, measured in kg·m²; M is mass, measured in kg; L is length, measured in m.

How is the Moment of Inertia (Rod, Center) formula derived?

I = ∫r²dm. For a rod: I = ∫₋L/2^L/2 x²(M/L)dx = (1/12)ML². The result is I = 1/12ML².