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Moment of inertia of a ring
Intermediate
All mass at radius R.
I = mR²A thin ring about its centre axis: I = mR², because all mass is at distance R.
A 2 kg bicycle rim of 0.35 m: 0.245 kg·m².
About a diameter it is ½mR².
In more detail
For a thin ring of mass M and radius R rotating about its central axis, I = MR². All the mass is at the same distance from the axis, so this is the largest moment for that radius.
Real-world uses
- Hoops and rims have a large moment of inertia, which keeps them spinning.
- Flywheel rings are designed to store large amounts of energy.
- A bicycle wheel is close to a ring, so its moment of inertia is mostly due to the mass on the rim.
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Frequently asked questions
Why is a ring harder to spin than a disc?
Because the mass is further from the axis for the same total mass.
Is MR² always the answer for a hoop?
Yes, for a thin hoop rotating about its central axis.
Why do wheel rims get heavier at the edge?
Mass far from the axis contributes much more to the moment of inertia, which is why racing wheels concentrate mass on the rim.
Related topics in Rotational Motion
Stability and toppling · Moment of inertia · Moment of inertia of a rod · Moment of inertia of a disc · Moment of inertia of a solid sphere · Moment of inertia of a hollow sphere