Parallel Axis Theorem
I_cm of a disc is (1/2)MR². Moment of inertia about tangent in plane of disc?
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About This Question
- Subject
- physics
- Chapter
- rotational motion
- Topic
- parallel axis theorem
- Difficulty
- Hard
- Year
- 2025
Solution
Correct Answer:
(5/4)MR²
- Identify Axis: The question asks about an axis in the plane of the disc that is tangent to the edge.
- Step 1: Moment about Diameter (Id):
- By the Perpendicular Axis Theorem, Icenter−perpendicular=Idia,x+Idia,y.
- 21MR2=2Id⟹Id=41MR2.
- Step 2: Apply Parallel Axis Theorem: The tangent in the plane is parallel to a diameter and is at distance R from the center.
- Itangent=Icm,parallel+Md2
- Itangent=41MR2+MR2
- Calculation: Itangent=(1/4+1)MR2=45MR2.
- Conclusion: The moment of inertia is (5/4)MR2.
This hard difficulty physics question is from the chapter rotational motion, covering the topic of parallel axis theorem. It appeared in the 2025 exam.
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