Get available formats for the youtube video:

[mumrik@snusmumriken ~]$ youtube-dl -F
[youtube] BvId5-0295U: Downloading webpage
[youtube] BvId5-0295U: Downloading video info webpage
[youtube] BvId5-0295U: Extracting video information
[youtube] BvId5-0295U: Downloading MPD manifest
[info] Available formats for BvId5-0295U:
format code  extension  resolution note
140          m4a        audio only DASH audio  137k , m4a_dash container, mp4a.40.2@128k (44100Hz), 162.65MiB
160          mp4        256x144    DASH video  126k , avc1.4d400c, 30fps, video only, 127.46MiB
133          mp4        426x240    DASH video  275k , avc1.4d4015, 30fps, video only, 281.09MiB
134          mp4        640x360    DASH video  342k , avc1.4d401e, 30fps, video only, 257.88MiB
135          mp4        854x480    DASH video  690k , avc1.4d401f, 30fps, video only, 538.66MiB
136          mp4        1280x720   DASH video 1392k , avc1.4d401f, 30fps, video only, 1.05GiB
17           3gp        176x144    small , mp4v.20.3,  mp4a.40.2@ 24k
36           3gp        320x180    small , mp4v.20.3,  mp4a.40.2
43           webm       640x360    medium , vp8.0,  vorbis@128k
18           mp4        640x360    medium , avc1.42001E,  mp4a.40.2@ 96k
22           mp4        1280x720   hd720 , avc1.64001F,  mp4a.40.2@192k (best)

-F: show available formats for the youtube video.

Get the URL for the youtube video format you want:

[mumrik@snusmumriken ~]$ youtube-dl -g -f 22!

-f: the format of the video, the number in the first column in the output of thе previous command.
-g: do not download but just output video’s URL.

Copy the URL exactly and entierly!

Now record that part of the video you want using ffmpeg:

[mumrik@snusmumriken ~]$ ffmpeg -i 'PASTE_HERE_URL_FOR_THE_VIDEO' -ss 1:10:05 -t 00:07:35 -c copy part.mp4

-ss: start point form where your recording will begin
-t: duration of the part you want to record