Answer: 3.65 m
Explanation:
from the question we have
angular speed = 33.3 rpm
coefficient of static friction (μ) = 0.3406
acceleration due to gravity (g) = 9.8 m/s^2
to get how far from the center of the turntable can the coin can be placed without having to slip off we equate the formula for the centrifugal force with the frictional force on the turntable force
mv^2 / r = m x g x μ
v^2 / r = g x μ .......equation 1
where
velocity (v) = angular speed (rads/seconds) x radius
we have to convert the angular speed from rpm to rads/seconds
angular speed (rads/seconds) = (2π / 60 ) x rpm
angular speed (rads/seconds) = ((2 x π) / 60 ) x 33.3 = 3.49 rads/ seconds
now
velocity = 3.49 x r = 3.49r
now substituting the value of velocity into equation 1
v^2 / r = g x μ
(3.49r)^2 / r = 9.8 x 0.3406
12.18 x r = 3.34
r = 3.65 m