A coin lies on the disk, which rotates uniformly, the coefficient of friction is η = 0.25, the angular velocity

A coin lies on the disk, which rotates uniformly, the coefficient of friction is η = 0.25, the angular velocity is ω = 5.0 rad / s. Find the maximum distance between the center of the coin and the axis of rotation at which the coin does not fly off.

The center of the coin is at a distance r from the axis of rotation. Then the coin moves in a circle with centripetal acceleration
a = ω ^ 2 * r;
This acceleration is imparted to the coin by a friction force, which is equal to:
F = η * m * g,
where m is the mass of the coin,
g = 10m / s ^ 2 – free fall acceleration;
According to Newton’s second law:
η * m * g = m * a = m * ω ^ 2 * r;
r = η * g / ω ^ 2 = 0.25 * 10/25 = 0.1m.