$1.$ Solve the following gear system design problem. The distant between the shafts is $100$ mm $.(50$ pt$)$

$1\mathrm{.}1.$ We have a motor that can rotate the driving shaft at $10$ Nm $.$ We want to transfer $30$ Nm to the driven shaft. Find the radius of pitch circles of the driving shaft gear and the driven shaft gear. $(10$ pt$)$

$1\mathrm{.}2.$ We are planning to use the gears that have pressure angle $\backslash (\backslash$phi$=20^\{\backslash$circ$\}\backslash ).$ Find the magnitude of the total force applied from the driving gear to the driven gear. $(10$ pt$)$

$1\mathrm{.}3.$ Find the smallest module for the gear design based on the following table $(10$ pt $)$

$1\mathrm{.}4.$ From the module we choose on problem $1\mathrm{.}3,$ find the number of teeth for both gears. $(10$ pt$)$

$1\mathrm{.}5.$ Calculate the addendum circle diameters for both gears. $(10$ pt$)$