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Mechanics
Mechanics

Moment of Inertia (Disk/Cylinder)

I=12MR2I = \frac{1}{2}MR^2

Moment of inertia of a solid disk or cylinder rotating about its central axis.

Variables

I
Moment of inertia
Rotational inertia
kg·m²
M
Mass
Total mass of disk
kg
R
Radius
Radius of disk
m

Derivation

I = ∫r²dm. For a disk with uniform density: I = ∫₀^R r²(2πrρh)dr = ½MR².

Your notes

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Common questions

What is the Moment of Inertia (Disk/Cylinder) formula?

Moment of Inertia (Disk/Cylinder) is written I = 1/2MR². Moment of inertia of a solid disk or cylinder rotating about its central axis. It belongs to Mechanics, under Rotational Motion.

What are the units in I = 1/2MR²?

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

How is the Moment of Inertia (Disk/Cylinder) formula derived?

I = ∫r²dm. For a disk with uniform density: I = ∫₀^R r²(2πrρh)dr = ½MR². The result is I = 1/2MR².