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Milo Martian
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But won't mechanical energy change due to friction? just curiousllober said:
Which will reach the bottom faster: solid or hollow sphere?
- Thread starter Milo Martian
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SUMMARY
The discussion centers on the dynamics of a solid sphere versus a hollow sphere of equal mass (M) and radius (R) rolling down an incline without slipping. Key equations include the center of mass acceleration (acm = Fext/M) and the moments of inertia for the hollow sphere (Ihollow = 2MR²/3) and solid sphere (Isolid = 2MR²/5). The solid sphere accelerates faster due to its lower moment of inertia, leading to a higher angular acceleration despite both spheres experiencing the same net external force. The confusion arises from the relationship between translational and rotational motion in pure rolling scenarios.
PREREQUISITES- Understanding of Newton's laws of motion
- Familiarity with rotational dynamics and torque
- Knowledge of moments of inertia for different shapes
- Concept of pure rolling motion and static friction
- Study the relationship between linear acceleration and angular acceleration in rolling objects
- Learn how to derive equations of motion for both translational and rotational dynamics
- Explore the implications of static friction in rolling motion scenarios
- Investigate the effects of different shapes on moment of inertia and rolling behavior
Physics students, educators, and anyone interested in classical mechanics, particularly in understanding the dynamics of rolling objects on inclines.