How do I find out about the shutter speed of frames in a video? I shot a video at 24FPS, and I want to find out what the shutter speed of each frame was. Quicktime Player and VLC's Info panels don't give me this information.

Neither does exiftool. Here's exiftool's output:

ExifTool Version Number         : 10.36
File Name                       : 24 FPS at 480p.mov
Directory                       : /Users/kartick/Desktop/Google Drive/Photos/Comparisons/Night Video Comparison
File Size                       : 7.7 MB
File Modification Date/Time     : 2017:04:18 19:55:15+05:30
File Access Date/Time           : 2017:05:05 06:57:31+05:30
File Inode Change Date/Time     : 2017:04:24 11:25:17+05:30
File Permissions                : rwxr-xr-x
File Type                       : MOV
File Type Extension             : mov
MIME Type                       : video/quicktime
Major Brand                     : Apple QuickTime (.MOV/QT)
Minor Version                   : 0.0.0
Compatible Brands               : qt
Movie Data Size                 : 8037178
Movie Data Offset               : 36
Movie Header Version            : 0
Create Date                     : 2017:04:18 14:25:15
Modify Date                     : 2017:04:18 14:25:38
Time Scale                      : 600
Duration                        : 22.75 s
Preferred Rate                  : 1
Preferred Volume                : 100.00%
Preview Time                    : 0 s
Preview Duration                : 0 s
Poster Time                     : 0 s
Selection Time                  : 0 s
Selection Duration              : 0 s
Current Time                    : 0 s
Next Track ID                   : 3
Track Header Version            : 0
Track Create Date               : 2017:04:18 14:25:15
Track Modify Date               : 2017:04:18 14:25:38
Track ID                        : 1
Track Duration                  : 22.75 s
Track Layer                     : 0
Track Volume                    : 100.00%
Image Width                     : 640
Image Height                    : 480
Clean Aperture Dimensions       : 640x480
Production Aperture Dimensions  : 640x480
Encoded Pixels Dimensions       : 640x480
Graphics Mode                   : ditherCopy
Op Color                        : 32768 32768 32768
Compressor ID                   : avc1
Source Image Width              : 640
Source Image Height             : 480
X Resolution                    : 72
Y Resolution                    : 72
Compressor Name                 : H.264
Bit Depth                       : 24
Video Frame Rate                : 24.004
Matrix Structure                : 1 0 0 0 1 0 0 0 1
Media Header Version            : 0
Media Create Date               : 2017:04:18 14:25:15
Media Modify Date               : 2017:04:18 14:25:38
Media Time Scale                : 44100
Media Duration                  : 22.80 s
Media Language Code             : und
Balance                         : 0
Handler Class                   : Data Handler
Handler Vendor ID               : Apple
Handler Description             : Core Media Data Handler
Audio Format                    : mp4a
Audio Channels                  : 1
Audio Bits Per Sample           : 16
Audio Sample Rate               : 44100
Purchase File Format            : mp4a
Handler Type                    : Metadata Tags
Software                        : ProCamera 10.2
Make                            : Apple
Model                           : iPhone 7 Plus
Avg Bitrate                     : 2.83 Mbps
Image Size                      : 640x480
Megapixels                      : 0.307
Rotation                        : 0


I tried saving a frame to an image file in VLC, but it saved without metadata, so I couldn't figure the shutter speed out.

I know the shutter speed is usually 1/48s (half of 1/frame rate), but this video was shot at night, so I want to check if the camera app used a longer shutter speed.
If the data was recorded by the camera as EXIF MetaData, Adobe Bridge would reveal the camera settings under the Metadata Panel. You may have to customize within Bridge WHICH metadata you want to look at; because there are literally hundreds, thousands, of types of EXIF data; which could or could not have been embedded; AND at times; you will find what you need hidden in a strange EXIF container. 

Simply put; if you don't see a shutter speed setting under MAIN, or CAMERA metadata; the brand camera/type, could have written it elsewhere; so show all; expand all, and scroll down to see if the data is possibly there; hidden in a collapsed field. 

If you shot the video at 24fps; you are right in thinking that it likely was recorded at 1/48 / 180 shutter. However; I would think; just based off the engineering / camera / lens type which is built onto the iPhone 7; and how I would engineer the camera to work using, which it does by default-  auto-exposure; that it would rely on aperture priority for exposure; and would thus constantly adjust your shutter speed on the fly based on it's exposure method. So if you did a constant shot from a dark area to bright area; you'd literally see an on the fly adjustment from 1/48 all the way up to 1/4000 or higher. Then aperture might kick in, as the phone as no ND filters to fall back on. 

I only add that because usually iPhone footage shot outdoors in bright sunlight looks like it was recorded at HIGH shutter (strobe effect) rather than iris down. The diameter on the lens of an iPhone 7 also would make me think they would use Aperture Priority (constant) as it's practically a pin-hole camera to begin with. 

Cheers!