Question

A wagon wheel is constructed as shown in the figure (Figure 1) . The radius of the wheel is 0.300 m, and the rim has mass 1.37 kg . Each of the eight spokes, that lie along a diameter and are 0.300 m long, has mass 0.250 kg .

What is the moment of inertia of the wheel about an axis through its center and perpendicular to the plane of the wheel?

Answer 1

required moment of inertia is I = I1+I2

I1 = moment of inertia of the rim

and I2 is the moment of inertia of the eight spokes

then I1 = M*R^2 = (1.37*0.3^2) = 0.1233 kg -m^2

I2 = 8*(1/3)*m*L^2 = 8*(1/3)*0.25*0.3^2 = 0.06 kg-m^2

I = 0.1233+0.06 = 0.1833 kg-m^2