To maintain a constant data read rate, the linear velocity of the DVD must remain constant. Since the circumference of the disk increases as the radius increases, the rotational speed must also increase as we move from the center to the outer edge. The linear velocity is given by:
v = ωr
where v is the linear velocity, ω is the rotational speed in radians per second, and r is the distance from the center of the disk.
Since we want to maintain a constant linear velocity, we have:
v = constant
ω1r1 = ω2r2
where ω1 is the rotational speed at the center of the disk, r1 is the radius of the center of the disk, ω2 is the rotational speed at the outer edge of the disk, and r2 is the radius of the outer edge of the disk.
We know that the disk spins at 1600 rpm for information at the center of the DVD. Let's assume that the radius of the center of the disk is 1 cm, and the radius of the outer edge of the disk is 6 cm. Then we have:
ω1 = 1600 rpm = 167.55 rad/s
r1 = 1 cm
r2 = 6 cm
Substituting these values into the equation above, we can solve for ω2:
ω1r1 = ω2r2
167.55 x 1 = ω2 x 6
ω2 = 27.92 rad/s
Finally, we can convert the angular velocity to rpm:
ω2 = 27.92 rad/s x 60 s/min ÷ 2π rad = 266.08 rpm
Therefore, the rotational speed of the disk needs to be 266.08 rpm at the outer edge of the DVD to maintain a constant data read rate.