A solid shaft of $30mm$ diameter and $3m$ long is made of low$-$carbon steel. Determine the shaft critical speed without load.

$($i$)$ Density of the shaft $r(\frac{kg}{m^3})=?$

$($ii$)$ Modulus of elasticity $E(GPa)=?$

$($iii$)$ Critical speed $(ra\frac{d}{s})=?$

$($iv$)$ Critical speed $(rpm)=?$

Answer:

$($iv$)n$