Pure Rolling Acceleration
A uniform solid cylinder (I = (1/2) m r^2) rolls down incline of angle θ without slipping. Linear acceleration is (g=gravity):
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About This Question
- Subject
- physics
- Chapter
- rotational motion
- Topic
- pure rolling acceleration
- Difficulty
- Hard
- Year
- 2025
Solution
Correct Answer:
(2/3) g sinθ
The linear acceleration a for an object rolling down an incline without slipping is: a=1+βgsinθ where β=mr2I For a solid cylinder, I=21mr2, so β=21. a=1+1/2gsinθ=3/2gsinθ=32gsinθ. Note: This acceleration is less than gsinθ (acceleration of sliding) because some of the potential energy is converted into rotational kinetic energy.
This hard difficulty physics question is from the chapter rotational motion, covering the topic of pure rolling acceleration. It appeared in the 2025 exam.
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