Why Is My Calculation of the Wheel's Moment of Inertia Incorrect?

[dannee]

Homework Statement

i've attched a picture of the wheel, which need to calculate moment of intertia with respect to 8 rods.

i've tried to use stiener rule but it's not getting the answer,

moment of wheel is (m1*r^2)/2
moment of rod is (m2*r^2/3)

i use the rule i total = icm + mr^2

so it's 8*( (m1*r^2)/2 + (m2*r^2)/3 )

what am i missing?

Homework Equations

m1 = mass of wheel
m2 = mass of rod
r = length of rod

The Attempt at a Solution

 

[Doc Al]

moment of wheel is (m1*r^2)/2

Revisit this formula.

so it's 8*( (m1*r^2)/2 + (m2*r^2)/3 )

There are 8 spokes but only 1 wheel.

 

[dannee]

that's right, 8 * 3(m2*r^2), i refer the moment of wheel is (m1*r^2)/2 and sum them,

but the correct answer is (3m2/8 + m1) * r^2

 

[Doc Al]

that's right, 8 * 3(m2*r^2), i refer the moment of wheel is (m1*r^2)/2 and sum them,

(1) Your formula for the moment of inertia of the wheel portion is incorrect.
(2) In your final result in post #1 you multiplied all terms by 8, thus counting the wheel 8 times.

but the correct answer is (3m2/8 + m1) * r^2

Double check that answer; looks like a typo.