QUESTION $5$

A $1\mathrm{.}25$ t flywheel rolls on parallel flat surfaces on it's $150$ mm diameter shaft. It is

arranged to oscillate, rolling through a small angle, by adding a mass of $160$ kg at $400$

mm radius from the shaft centre and the oscillations are timed at the rate of $100$ per

$499$ s$.$

a$)$ Calculate the radius of gyration of the flywheel alone about it's own centroidal

axis. $(0\mathrm{.}545m)$

b$)$ Find the approximate period of oscillation, with the same offset loading but with

the flywheel rolling on it's own $625$ mm radius rim instead of on the $150$ mm

shaft. $(7\mathrm{.}4$ s$)$