Teaching Physics with the Physics Suite Edward F. Redish

A CD for a computer stores information by magnetizing small regions of the disk. For a typical disk, estimate the area of the disk that corresponds to a single bit of information. (Remember: the storage capacity of a disk is usually given in bytes where 1 byte = 8 bits.)

Solution

Using the first digit of my thumb to measure, I find that a typical floppy disk has a radius of about 2 inches. This is about (2 in) x (2.54 cm/in) or about 5 cm. This implies an area of πR² = about 3 x 5 cm x 5 cm or about 75 cm². The disks I use hold 800 MB of information. This is 800 x 10⁶ bytes = 8 x 10⁸ bytes x (8 bits/byte) = about 6.4 x 10⁹ bits. These bits are distributed over an area of 75 cm² (= 75 x 10^-4 m² = 7.5 x 10^-3 m²) so, assuming that each bit has its own space and there is no overlap, each bit must occupy a space of (7.5 x 10^-3 m²) / (6.4 x 10⁹ bits) = 1.2 x 10^-12 m². If we think of this as a tiny square, it has dimensions Sqrt(1.2) x 10^-6 m or about 1 micrometer on a side.

Page last modified May 29, 2011: G12