Question 1206775
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<pre>

The invariant is the product  {{{r*alpha}}},  the radius times the angle.


So, we write  

    {{{r*alpha}}}  = {{{R*beta}}},

or

    {{{10*alpha}}} = 100*60.


From this equality, we find

    {{{alpha}}} = {{{(100*60)/10}}} = 10*60 = 600 degrees = 360 degrees + 240 degrees,


so the small wheel will make one full rotation and 2/3 of the other rotation.
</pre>

Solved.