Question

Consider a flywheel whose mass M is distributed almost equally between a heavy, ring-like rim of radius R and a concentric dislike feature of radius R/2. Other parts of the flywheel, such as spokes, etc, have negligible mass. The best approximation for $\alpha$, if the mass moment of inertia of the flywheel about its axis of rotation is expressed as $\alpha M{R}^2$is

• A. 0.56

Answer 1

The correct option is A 0.56
Given : Radius of rim = R
Radius of disk = R/2

Average radius of flywheel
$=\frac{(R+\frac{R}{2})}{2}=\frac{\left(\frac{3R}{2}\right)}{2}=\frac{3R}{4}$

Mass moment of inertia,
$I_0=M{\left(\frac{3R}{4}\right)}^2$

$I_0=\frac{9}{16}M{R}^2$ ....(i)

Given, $I_0=\alpha M{R}^2$ ....(ii)

On comparing equation (i) and (ii), we get

$\alpha =\frac{9}{16}=0.5625\approx 0.56$