Key relationship
I = βMr²; k = √(I/M). βring=1, βdisc=½, βsphere=2/5, βrod=1/12.
Physics · Class 11
Compare shapes around an axis
Moment of inertia depends on how mass is distributed relative to an axis. More mass farther from the axis increases I. Radius of gyration is the single effective radius that reproduces I= Mk².
Open the interactive experiment →Compare shapes around an axis
அச்சிலிருந்து நிறை எவ்வளவு தொலைவில் பரவியுள்ளது என்பதை நிலைமத் திருப்புத்திறன் காட்டுகிறது.
Key notes, relationships and model limits
Remember
Moment of inertia depends on how mass is distributed relative to an axis. More mass farther from the axis increases I. Radius of gyration is the single effective radius that reproduces I= Mk².
Common trap
Moment of inertia is tied to an axis, not only a mass and shape.
Model limits
Ring/disc/sphere about symmetry axes; uniform rod about its midpoint perpendicular to its length. For rod, the radius slider specifies its full length.
What you will learn
Compare shape-dependent inertia and radius of gyration.
Try the experiment
Try both scenarios, change one control, and predict the result before checking the graph and readouts.
Think of it this way
Change one input while keeping the others fixed, as you would in a controlled experiment.
Worked example
At M=2 kg and r=1 m, disc I=1 kg·m² and k=0.707 m; ring I=2 kg·m² and k=1 m.
Why this matters
The model connects compare shapes around an axis with an observable reading. Check the equation and assumptions before applying it.
Before you start
SI units · algebra · graph reading
Check your understanding
For the same mass and radius, which has greater I: ring or solid disc?
- The disc has twice the ring inertia
- The ring has twice the disc inertia
- They have equal inertia
Read the explanation
Iring=Mr² and Idisc=½Mr².
Course connection: Class XI Chapter 6. Consult the roadmap for CBSE, NEET, JEE Main and Advanced scope.