Moment of Inertia of a Wagon Wheel

AI Thread Summary
The moment of inertia of a wagon wheel involves calculating contributions from both the rim and the spokes. The rim's moment of inertia is calculated using the formula I = mass times radius squared. However, for the spokes, which can be treated as thin rods, a different approach is needed, as their mass is distributed along their length. The correct calculation simplifies the process significantly. Understanding the distinction between the rim and spokes is crucial for accurate computation.
Trojanof01
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A wagon wheel is constructed as shown in the figure. The radius of the wheel is 0.300 m, and the rim has mass 1.36kg . Each of the eight spokes, that lie along a diameter and are 0.300 m long, has mass 0.270kg .

What is the moment of inertia?


Wouldn't it just be the sum of the masses times the radius squared?

I = 1.36(.300)^2 + .8(.270(.300^2))
 
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Trojanof01 said:
Wouldn't it just be the sum of the masses times the radius squared?
For the rim, yes; for the spokes, no. The mass of the rim is all at a single distance from the axis; not so for the mass of the spokes. Hint: Look up (or figure out) the moment of inertia of a thin rod about one end. (Treat the spokes as thin rods.)
 
Oh! /smack That made that so much more simple. Thanks much.
 
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