Moment of Inertia of a Wagon Wheel

[Trojanof01]

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))

 

[Doc Al]

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.)

 

[Trojanof01]

Oh! /smack That made that so much more simple. Thanks much.