91Ó°ÊÓ

The mass of the wheel is \(m = 1.1\;{\rm{kg}}\).

The diameter of the wheel is \(d = 67\;{\rm{cm}} = 0.67\;{\rm{m}}\).

Moment of inertia is a quantity that expresses a body’s tendency to resist angular acceleration about the axis of rotation.

It is given as the product of the mass of a rigid body and the square of the distance from the axis of rotation.

\(I = m{r^2}\)

Consider the rim and the tire as a hoop where all of the significant masses are located at the same distance \(\left( {r = \frac{d}{2}} \right)\) from the axis of rotation. Thus, the moment of inertia of the wheel will be given by:

\(\begin{align}I &= m{r^2}\\ &= \left( {1.1\;{\rm{kg}}} \right){\left( {\frac{{0.067}}{2}\;{\rm{m}}} \right)^2}\\ &= \left( {1.1\;{\rm{kg}}} \right){\left( {0.335\;{\rm{m}}} \right)^2}\\ &= 0.12\;{\rm{kg}}\;{{\rm{m}}^2}\end{align}\)

The mass of the hub can be ignored because its distance from the axis of rotation is significantly less (approximately r = 0). So, it has a very small rotational inertia.