A small button placed on a horizontal rotating platform with diameter $0\mathrm{.}320$ m will revolve with the platform when it is brought up to a speed of $40$ rev$/$min$,$ provided the button is no more than $0\mathrm{.}150$m from the axis.

$($a$)$ What is the coefficient of static friction between the button and the platform?

$($b$)$ How far from the axis can the button be placed, without slipping, if the platform rotates at $60$ rev$/$min$?$