A wheel is rotating freely at angular speed $910re\frac{v}{m}in$ on a shaft whose rotational inertia is negligible. A second wheel, initially at rest and with $6$ times the rotational inertia of the first, is suddenly coupled to the same shaft. $($a$)$ What is the angular speed of the resultant combination of the shaft and two wheels? $($b$)$ What fraction of the original rotational kinetic energy is lost?

$($a$)$ Number $$ Units

$re\frac{v}{m}in$

$($b$)$ Number $$ Units

No units