Which has the larger moment of inertia?

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Homework Help Overview

The discussion revolves around comparing the moment of inertia of two wheels: a uniform disk and a bicycle wheel with spokes, both having the same total mass and radius. Participants explore how the distribution of mass affects the moment of inertia.

Discussion Character

  • Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the definition of moment of inertia and its dependence on mass distribution. Some attempt to relate the moment of inertia to the geometry of the objects, while others question how the mass distribution impacts the overall inertia.

Discussion Status

There is an ongoing exploration of the relationship between mass distribution and moment of inertia. Some participants have provided insights into the calculations for different shapes, suggesting that the bicycle wheel may have a larger moment of inertia due to its mass being concentrated further from the axis of rotation.

Contextual Notes

Participants are working with the assumption that both wheels have the same mass and radius, but there is a discussion about the implications of their different structures on the moment of inertia.

eraemia
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Homework Statement



Two wheels have the same total mass M and radius R. One wheel is a uniform disk. The other is like a bicycle wheel, with lightweight spokes connecting the rim to the hub. Which has the larger moment of inertia?

a. The solid disk
b. The wheel with spokes
c. There is insufficient unformation for a meaningful answer

Homework Equations





The Attempt at a Solution



the solid disk because it has less surface area / holes for air friction?
 
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Think about the definition of moment of inertia... it is [tex]\int{dm*r^2}[/tex]
 
ok so the thin spherical shell would have a moment of inertia of 2/3 MR^2
whereas the solid sphere would have 2/5 MR^2

therefore the bicycle has more inertia
 
eraemia said:
ok so the thin spherical shell would have a moment of inertia of 2/3 MR^2
whereas the solid sphere would have 2/5 MR^2

therefore the bicycle has more inertia

Yes, exactly right. More of the mass is concentrated at a larger radius in the bicycle...

For the uniform disk, a lot of the mass is in between 0 and R... but for the bicycle most of it is located around R... so the integral dm*R^2 is higher for the bicycle.
 
alright, i think i get it now. thanks
 

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