The solution to the problem can be found in NTSC's interlaced format. Because a full frame of NTSC video consists of two interlaced fields, instead of speeding up the film source, individual fields (half frames) can be duplicated in a regular pattern, resulting in the correct framerate without a speed increase. To understand how this works it's best to start by assuming a video framerate of 30fps.
When color was added to create NTSC color television, the original U.S. television framerate of 30fps was reduced by 0.1% in order to add the new color information to each broadcast. Since 24 and 30 have a common factor of 6 (6 x 4 = 24 and 6 x 5 = 30), a simple field duplication pattern called telecine can be used to make 24fps film content use 60 video fields (30 frames). That means if 1 in 4 frames is repeated 24fps becomes 30fps.
Since NTSC is actually transmitted at 59.94 interlaced fields (half frames) per second, only half frames need to be duplicated, making it smoother since the repeated picture elements are spread more evenly through the video. Reducing the speed by 0.1% yields 23.976fps. The repeated fields calculated for the conversion from 24fps to 30fps will change it to 29.97fps NTSC video.
The telecine process was developed for broadcast television, but the requirements for digital video, such as DVD, destined for playback on analog NTSC televisions are the same - with one major exception. Unlike analog video, where fields must be recorded multiple times to be duplicated, digital video can simply include instructions for a decoder to create duplicates. Not only does this reduce storage requirements by eliminating redundant data, but it also increases quality at a given bitrate or bitrate at a given quality.
Digital Video Fundamentals
If you're new to digital video, or just want a refresher on the basics, you may want to start with the other guides in our Digital Video Fundamentals guides before going any further. This series of guides covers basic subjects ranging from color to resolution and frame structure. In particular you should make sure to read the Frames and Framerates guide if you don't already have a basic understanding of progressive and interlaced frames, as well as NTSC and film framerates.