A solid disk of radius \(R = 0.40 \text{ m}\) starts from rest at time \(t = 0 \text{ s}\) and rotates about a fixed central axis with a constant angular acceleration of \(\alpha = 5.0 \text{ rad/s}^2\). A point is located on the outer rim of the disk. Through what angular displacement has the disk rotated when the magnitude of the centripetal acceleration of the point equals the magnitude of its tangential acceleration?