Why Does a Cylinder Have the Least Moment of Inertia Compared to a Ring?

AI Thread Summary
A cylinder has the least moment of inertia compared to a ring due to its mass distribution being closer to the axis of rotation. The moment of inertia (MOI) quantifies how mass is distributed relative to an axis, affecting an object's resistance to rotational motion. For a cylinder, more mass is concentrated near the center, leading to a lower MOI. In contrast, a ring has a greater moment of inertia because its mass is distributed further from the axis. Understanding these principles is essential for analyzing rotational dynamics in physics.
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Could somebody please explain why the cylinder has the least moment of intertia about the axis? And which one has the greatest, the ring?
 

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You have to do the integral to find that out, or look up their values online. Do you know what MOI means?
 
Big hint: The moment of inertia is the description of how mass is distributed about an axis.
 

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