Parallel Axis Theorem
The moment of inertia of a disc of mass M and radius R about its center is MR²/2. What is its moment of inertia about a tangent in its plane?
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About This Question
- Subject
- physics
- Chapter
- rotational motion
- Topic
- parallel axis theorem
- Difficulty
- Hard
- Year
- 2025
Solution
Correct Answer:
5MR²/4
- Step 1: Disc Diameter: By the perpendicular axis theorem (Iz=Ix+Iy), for a symmetric disc, Iz=2Idiameter.
- Idiameter=Iz/2=(MR2/2)/2=MR2/4.
- Step 2: Axis Selection: A tangent in the plane is parallel to the diameter.
- Step 3: Parallel Axis Theorem: Itangent=Idiameter+Mh2, where h=R.
- Calculation:
- I=4MR2+MR2=45MR2.
- Note: If the tangent was perpendicular to the plane, the starting axis would be the center axis (MR2/2), giving 3MR2/2.
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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