Answer:
the coin does not slide off
Explanation:
mass (m) = 5 g = 0.005 kg
distance (r) = 15 cm = 0.15 m
static coefficient of friction (μs) = 0.8
kinetic coefficient of friction (μk) = 0.5
speed (f) = 60 rpm
acceleration due to gravity (g) = 9.8 m/s^{2}
lets first find the angular speed of the table
ω = 2πf
ω = 2 x π x 60 x [tex]\frac{1}{60}[/tex]
ω = 6.3 s^{-1]
Now lets find the maximum static force between the coin and the table so we can get the maximum velocity the coin can handle without sliding
static force (Fs) = ma
static force (Fs) = μs x Fn = μs x m x g
Fs = 0.8 x 0.005 x 9.8 = 0.0392 N
Fs = ma
0.0392 = 0.005 x a
a = 7.84 m/s^{2}
[tex](Vmax)^{2}[/tex] = a x r
[tex](Vmax)^{2}[/tex] = 7.84 x 0.15
Vmax = 1.08 m/s
ωmax = [tex]\frac{Vmax}{r}[/tex]
ωmax = [tex]\frac{1.08}{0.15}[/tex] = 7.2 s^{-1}
now that we have the maximum angular acceleration of the table, we can calculate its maximum speed in rpm
Fmax = [tex]\frac{ωmax}{2π}[/tex]
Fmax = [tex]\frac{7.2}{2 x π}[/tex] = 68.7 rpm
since the table is rotating at a speed less than the maximum speed that the static friction can hold coin on the table with, the coin would not slide off.
