Question

A disk has 128 tracks of 32 sectors each, on each surface of eight platters. The disk spins at 3600 RPM and takes 15 ms to move between adjacent tracks. What is the longest time needed to read an arbitrary sector located anywhere on the disk

Answer 1

To determine the total distance a piece of dust on a spinning CD travels, you calculate the path's circumference and multiply it by the number of revolutions made in the given time, resulting in the product of 2π(4.3) cm × 1500.

Step-by-step explanation:

Calculating Total Distance Traveled by Dust on a CD

To calculate the total distance traveled by a piece of dust on a CD that has a spin rate of 500 rpm and is located 4.3 cm from the center, we can use the formula for the circumference of a circle, C = 2πr, where r is the radius. Since we're given the spin rate in revolutions per minute (rpm) and the time in minutes, we first convert the time to the same units that our speed is in - revolutions. Hence, 3 minutes at 500 rpm equals 1500 revolutions.

Now, we calculate the circumference of the path which the dust particle takes as it is located 4.3 cm from the center. The circumference is therefore C = 2π(4.3) cm. When we multiply the circumference by the number of revolutions, we get the total distance traveled:

Total distance = Circumference × Number of revolutions
= 2π(4.3) cm × 1500
= 2π(4.3) cm × 1500

Finally, we calculate the above expression to find the total distance traveled by the dust particle.

Answer 2

the longest time needed to read an arbitrary sector located anywhere on the disk is 2971.24 ms

Step-by-step explanation:

Given the data in the question;

first we determine the rotational latency

Rotational latency = 60/(3600×2) = 0.008333 s = 8.33 ms

To get the longest time, lets assume the sector will be found at the last track.

hence we will access all the track, meaning that 127 transitions will be done;

so the track changing time = 127 × 15 = 1905 ms

also, we will look for the sectors, for every track rotations that will be done;

128 × 8.33 = 1066.24 ms

∴The Total Time = 1066.24 ms + 1905 ms

Total Time = 2971.24 ms

Therefore, the longest time needed to read an arbitrary sector located anywhere on the disk is 2971.24 ms