Answer:
The moment of inertia is calculated as 0.542 [tex]kgm^{2}[/tex]
Solution:
As per the question:
Mass of the rim, M = 1.5 kg
Radius of the rim, R = 0.50 m
No. of spokes, n = 8
Mass of each spoke, m = 0.25 kg
Now,
To calculate the moment of inertia about the center of the wheel and perpendicular to its plane:
[tex]I = I_{c} + I_{y}[/tex]
where
[tex]I_{c}[/tex] = Moment of Inertia about the center
[tex]I_{y}[/tex] = Moment of Inertia about an axis perpendicular to its plane
[tex]I = MR^{2} + n\frac{mR^{2}}{3}[/tex]
[tex]I = 1.5\times 0.50^{2} + 8\times\frac{0.25\times 0.50^{2}}{3} = 0.542\ kgm^{2}[/tex]
