Mechanics
Moment of Inertia (Disk/Cylinder)
Moment of inertia of a solid disk or cylinder rotating about its central axis.
Variables
Ikg·m²
Moment of inertia
Rotational inertia
Allowed values: 0 or more
Mkg
Mass
Total mass of disk
Allowed values: 0 or more
Rm
Radius
Radius of disk
Allowed values: greater than 0
Derivation
I = ∫r²dm. For a disk with uniform density: I = ∫₀^R r²(2πrρh)dr = ½MR².
Your notes
0/5000
Check value
Round inputs run through this page's calculator. Use it to test your own working or a rearranged form. It is a test case, not a real-world example.
- M = 2 kg (Mass)
- R = 3 m (Radius)
Result: I = 9 kg·m²
Other mechanics formulas with the same quantities
- 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 Rotational Kinematic 3 and before Moment of Inertia (Solid Sphere).
- 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 Moment of Inertia (Disk/Cylinder) formula?
Moment of Inertia (Disk/Cylinder) is written I = (1/2)MR². 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 = (1/2)MR²?
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 = (1/2)MR².