Key relationship
Iparallel = ICM+Md²; Iperpendicular = Ix+Iy for a planar lamina.
Physics · Class 11
Shift the rotation axis
Moving an axis parallel to the central axis adds Md² to inertia. For a thin planar body, the perpendicular-axis theorem adds two orthogonal in-plane inertias. These theorems refer to different axis relationships.
Open the interactive experiment →Shift the rotation axis
இணை அச்சு தேற்றத்தில் I = ICM + Md². தளத் தகட்டில் செங்குத்து அச்சின் திறன் இரண்டு தள அச்சுகளின் திறன்களின் கூட்டுத்தொகை.
Key notes, relationships and model limits
Remember
Moving an axis parallel to the central axis adds Md² to inertia. For a thin planar body, the perpendicular-axis theorem adds two orthogonal in-plane inertias. These theorems refer to different axis relationships.
Common trap
The perpendicular-axis theorem applies to planar laminae, not arbitrary 3D solids.
Model limits
Uniform thin disc. Ix and Iy are orthogonal in-plane central axes; Ic is their common perpendicular central axis.
What you will learn
Distinguish parallel and perpendicular axes and compute shifted inertia.
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
For this disc Ix=Iy=0.5 kg·m², so Ix+Iy=1 kg·m². Moving the normal axis 1 m raises it to 3 kg·m².
Why this matters
The model connects shift the rotation axis with an observable reading. Check the equation and assumptions before applying it.
Before you start
SI units · algebra · graph reading
Check your understanding
A 2 kg disc has central I=1 kg·m². What is I at offset 1 m?
- 1 kg·m²
- 3 kg·m²
- 2 kg·m²
Read the explanation
I=1+2×1²=3 kg·m².
Course connection: Class XI Chapter 6. Consult the roadmap for CBSE, NEET, JEE Main and Advanced scope.