Answer
(a) greater than
(b) $5.3\times 10^{-5}Kg.m^2$
Work Step by Step
(a) We know that $I=\frac{2r^2m}{v^2}(gh-\frac{1}{2}v^2)$. This equation shows that if more mass is concentrated near the rim of the yo-yo then its moment of inertia will be greater than that of its initial moment of inertia.
(b) We know that
$I=\frac{2r^2m}{v^2}(gh-\frac{1}{2}v^2)$
We plug in the known values to obtain:
$I=\frac{(2)(0.0064m)^2(0.056Kg)}{(0.64m/s)^2}[(9.8m/s^2)(0.50m)-\frac{1}{2}(0.64m/s)^2]$
This simplifies to:
$I=5.3\times 10^{-5}Kg.m^2$
