Question

A bicycle wheel of radius $0.3m$ has a rim of mass $1.0kg$ and $50spokes$, each of mass $0.01kg$. What is its moment of inertia about its axis of rotation?

Answer 1

Given,

Radius of wheel, $R=0.3m$

Mass of rim, $M=0.1kg$

Number of spokes, $N=50nos$

Mass of spokes, $m=0.01kg$

Length of spokes, $L=R=0.3m$

Moment of inertia of rim $=M{R}^2=1.0\times {\left(0.3\right)}^2=0.09kg{m}^2$
Moment of inertia of spokes $=N\frac{m{L}^2}{3}=50\times \frac{0.01\times {\left(0.3\right)}^2}{3}=0.015kg{m}^2$
Total moment of inertia $=0.09+0.015=0.105kg{m}^2$