Earlier techniques for low power speed control in disk drives running audio/video applications attempted to either match the drive's speed to the data rate requirement of the host application (just-in-time speed), or run it at the maximum drive speed, neither of which are energy-optimal in general. Starting from the theory of DC motors, we obtain a high-level power model of a disk drive. We then analytically obtain the speed profile (function of time) that minimizes the energy required to transfer a given amount of data from/to the drive, in a given amount of time. Based on a power model obtained by measurement from a commercial optical drive, it is estimated that the proposed speed control technique consumes 79%, 70% and 50% less energy for VCD, SVCD and DVD video playback, respectively, when compared to existing just-in-time CLV techniques. This work also provides an analytical framework to understand earlier observations that buffering multimedia data and employing CAV mode in disk drives is more energy-efficient.