Perpendicular Axis Theorem
Easyphysics
For a thin circular disc, if I_x = I_y = I (moments of inertia about two perpendicular diameters), what is the moment of inertia about the axis perpendicular to the plane through center?
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Solution
Incorrect! Answer:
2I
- Theorem Statement: For a 2D object, the inertia about a normal axis is the sum of inertias about two perpendicular axes in the plane.
- Relationship: Iz=Ix+Iy.
- Identify Context: For a disc, any diameter is an axis of symmetry, so Ix=Iy=I.
- Substitution: Iz=I+I=2I.
- Physical Case: If Idiameter=MR2/4, then Icenter−axis=2×MR2/4=MR2/2.
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About This Question
- Subject
- physics
- Chapter
- rotational motion
- Topic
- perpendicular axis theorem
- Difficulty
- Easy
- Year
- 2025
Solution
Correct Answer:
2I
- Theorem Statement: For a 2D object, the inertia about a normal axis is the sum of inertias about two perpendicular axes in the plane.
- Relationship: Iz=Ix+Iy.
- Identify Context: For a disc, any diameter is an axis of symmetry, so Ix=Iy=I.
- Substitution: Iz=I+I=2I.
- Physical Case: If Idiameter=MR2/4, then Icenter−axis=2×MR2/4=MR2/2.
This easy difficulty physics question is from the chapter rotational motion, covering the topic of perpendicular axis theorem. It appeared in the 2025 exam.
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