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Moment of inertia of a disc
Intermediate
Uniform disc about its axis.
I = ½mR²A uniform disc about its centre axis: I = ½mR². It is smaller than the ring since the mass is closer to the axis.
m = 4 kg, R = 0.5: 0.5 kg·m².
Same mass and radius as a ring has twice the I.
In more detail
For a uniform solid disc of mass M and radius R rotating about its central axis, I = ½MR².
Real-world uses
- Discs and pulleys are modelled with this moment of inertia.
- Turntables use disc inertia to stay spinning steadily.
- A flywheel in an engine is designed as a disc, which stores a large rotational energy for its mass.
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Frequently asked questions
Why is it half of MR²?
Because mass is spread over the disc, not all at the rim, so the average distance squared is smaller.
Does it matter whether the disc is thick?
Not for a thin uniform disc, as long as its mass is uniform.
Is a disc easier to spin up than a ring of the same mass and radius?
Yes. A disc has half the moment of inertia of a ring with the same mass and radius, so it accelerates faster.
Related topics in Rotational Motion
Moment of inertia · Moment of inertia of a rod · Moment of inertia of a ring · Moment of inertia of a solid sphere · Moment of inertia of a hollow sphere · Parallel axis theorem