A machine in the workshop has a spindle that rotates at $41\mathrm{.}887902ra\frac{d}{sec}$ when the input power is $2$ kW $.$ The spindle is made from $45$ C $8$ carbon steel with a modulus of rigidity of $84k\frac{N}{m}{m}^2$ and the maximum allowable angle of twist is $0\mathrm{.}25$ per meter length.

Determine the torque in the spindle.

$(2)$

Determine the radius of the spindle.

$(4)$

Determine the factor of safety$($FOS$)$ if the maximum allowable shear stress for the shaft is $5$ MPa $.$

$(4)$

Is the shaft diameter suitable for the spindle if the maximum allowable shear stress for the shaft is $10$ MPa $.$

$(2)$

$[12]$