Answer: 24.8 mm
Explanation:
The centripetal acceleration of the edge of the coin is given by:
[tex]a=\omega^2 r[/tex] (1)
where
[tex]\omega[/tex] is the angular frequency
r is the radius of the coin
The frequency of revolution of the coin is equal to the number of spins divided by the time taken:
[tex]f=\frac{18}{12 s}=1.5 Hz[/tex]
And the angular frequency is given by
[tex]\omega=2 \pi f=2 \pi (1.5 Hz)=9.42 rad/s[/tex]
Since we know the centripetal acceleration, [tex]a=2.2 m/s^2[/tex], we can re-arrange eq.(1) to find the radius of the coin:
[tex]r=\frac{a}{\omega^2}=\frac{2.2 m/s^2}{(9.42 rad/s)^2}=0.0248 m=24.8 mm[/tex]
