Final answer:
The disk's average angular acceleration is -1424.77 rad/s², and the magnitude of the tangential linear acceleration of a point on the disk's edge is 85.49 m/s².
Step-by-step explanation:
To calculate the magnitude of the average angular acceleration of the disk, we use the equation α = Δω / Δt, where α is the angular acceleration, Δω is the change in angular velocity, and Δt is the change in time. First, we need to convert the angular velocity from rpm to rad/s. The conversion factor is 2π rad/s per revolution, which gives us an initial angular velocity of ωi = 4210 rpm * (2π rad/s) / (60 s/min) = 441.68 rad/s. Since the disk comes to rest, the final angular velocity, ωf, is 0 rad/s. The change in angular velocity is Δω = ωf - ωi = -441.68 rad/s, and the change in time is Δt = 0.31 s. Thus, the average angular acceleration is α = -441.68 rad/s / 0.31 s = -1424.77 rad/s².
The magnitude of the tangential linear acceleration at a point on the disk's edge can be found using the equation at = α*r, where at is the tangential acceleration, α is the angular acceleration, and r is the radius of the disk. Given that the disk is 12.0 cm in diameter, the radius r is 6.0 cm or 0.06 m. Thus, the tangential linear acceleration is at = 1424.77 rad/s² * 0.06 m = 85.49 m/s².