Part 04 · Rotation and gravity · Card 5 of 11
Moment of inertia
How hard an object is to spin. It depends on mass and how far the mass sits from the axis, I = sum of m r squared.
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Analogy
A figure skater with arms out is harder to spin than with arms in.
Example
Single mass
I = m r^2I = 2 x 0.5^2I = 0.5 kg m^2
In practice
A 2 kg mass at 0.5 m from the axis has I = 0.5 kg m squared.
Practice
Flashcards
- What does a larger moment of inertia mean?The object is harder to start or stop spinning.
Interview questions
- A figure skater pulls her arms in. Explain the change in spin rate and kinetic energy.
- Angular momentum is conserved
- Moment of inertia falls so omega rises
- Kinetic energy increases because the skater does work
Questions people ask
Why does a hollow cylinder roll slower than a solid one?
A hollow cylinder has its mass farther from the axis, so it has a bigger moment of inertia. More of the energy goes into spinning and less into moving forward. Down the same ramp, a solid cylinder reaches the bottom first.
Does moment of inertia depend on the axis?
Yes. The same object has a different I about a different axis. A rod spun about its centre has I = ML squared over 12, but spun about its end it has ML squared over 3. Always state the axis before using a value.