YouTube has a built-in slow-motion option for its videos that is available when you use the HTML5 video player, rather than the default player. As long as you have an up-to-date version of Chrome, Firefox, Internet Explorer, Opera or Safari, you can enable HTML5 and use YouTube's slow-motion feature. Chrome has the HTML5 video player enabled by default, but other browsers typically require this setting to be manually enabled.
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After loading a YouTube video, click the Setting gear icon just below the video image. Click the drop-down menu beside the Speed selector option, where you can choose "0.25" or "0.5" for one-quarter or one-half speed. If the Speed selector option is not available, the HTML5 video player may be disabled. Check the YouTube HTML5 Video Player page and ensure that the box is checked beside "The HTML5 player is currently used when possible."
To enable the HTML5 video player, visit the YouTube HTML5 Video Player page and click the button labeled "Request the HTML5 player." If you instead see a button labeled "Use the default player," then the HTML5 video player is already enabled and you do not need to change anything. When you now view a YouTube video and click the Settings gear icon below the video image, you can use the Speed selector drop-down menu to choose "0.25" for one-quarter speed or "0.5" for one-half speed.