# Which has the larger moment of inertia?

1. Sep 23, 2007

### eraemia

1. The problem statement, all variables and given/known data

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

2. Relevant equations

3. The attempt at a solution

the solid disk because it has less surface area / holes for air friction?

2. Sep 23, 2007

### learningphysics

Think about the definition of moment of inertia... it is $$\int{dm*r^2}$$

3. Sep 23, 2007

### eraemia

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

4. Sep 23, 2007

### learningphysics

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.

5. Sep 23, 2007

### eraemia

alright, i think i get it now. thanks