- #1
jamesbiomed
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Homework Statement
A wagon wheel is made entirely of wood. Its components consist of a rim, 16 spokes, and a hub. The rim has mass 5.1 kg, outer radius 0.90 m, and inner radius 0.86 m. The hub is a solid cylinder with mass 3.1 kg and radius 0.12 m. The spokes are thin rods of mass 1.1 kg that extend from the hub to the inner side of the rim. Determine the constant
c = I/MR2 for this wagon wheel.
Hi folks, this will be my last problem, promise.
Homework Equations
I for hub=> I for solid cylinder=> 1/2 M R^2
I for wheel=> I for thick hollow cylinder or wheel (I THINK...) =1/2 M (R1^2+R2^2)
Otherwise, I for hollow cylinder or hoop is MR^2
I for thin rod is 1/12 M h^2. These are rotating about their end though, so by parallel axis theorem, their moment is : 1/12Mh^2+M(h/2)^2
I(net)=cMR^2
c=I/MR^2
So there you have it.
The Attempt at a Solution
The correct answer is .356
My answer is .344
Here's what I did:
For Hub:1/2(3.1)*.12^2=.002232
For Wheel: 1/2(5.1)(.90^2+.86^2)=3.95148
For thin rods: 16 *{(1/12)(1.1)(.74)^2 + (.74/2)^2(1.1)}=3.212586
Then added them all to get 7.1832
Then divided them by their combined mass (16*1.1+5.1+3.1)=25.8 and the entire radius^2
so 7.1832/(25.8*.9^2)=.344
I've tried with less sig figs, and it doesn't work. There's something off, but its small. I have a feeling a quick once-over might spot it. Many thanks!