Webcams are going to require a computer to capture the video to. This can be done using a tool like VLC but it's going to take someone with a clue on how to plumb cameras into VLC instances and set up scripts to trigger video capture and the like.
It's going to be _much_ easier if you do this in the following fashion:
Buy ten identical action cameras. Brand doesn't matter as long as they don't get too hot during operation, if the LED screen turns off, etc. but I've done this with GoPro Hero 5s in a past life- you need a camera which can be operated (capture video and be mounted to the tripod) while it's plugged in. Get ten long USB charging cables and wall plugs, etc. Get ten tripods or other mounts for them (magnets, clamps, whatever fits for your deployment application.) Get twenty flash chips, two for each system, of a capacity where each can hold eight or more hours of video. Get two large external hard drives, connect them to the computer you'll be using, set them up to mirror each other (e.g. anything written to one is replicated to the second.) During the morning session, you'll have the cameras recording on the first set of flash drives, while you're pulling the recordings off the second set of flash drives from the prior afternoon's recordings. In the afternoon session, the cameras will have the second set of wiped drives back in them, and you'll pull the morning's recordings off the first set of drives.
Here's a little bash script you can use (on MacOS) to pull the files off of your drive and copy them to the external drives you'll want. You'll need to modify paths to match your setup. It concatenates all of the 12 minute GoPro videos into one large file in the process, and removes the originals at the end. You execute it with ./import_gopro.sh <value> where <value> is the camera number.
$ cat import_gopro.sh
#!/bin/bash
SUFFIX=`echo $1`
SRCDIR=`ls -d /Volumes/*|grep GOPRO`
DESTDIR="/Volumes/Dans_Personal_Drive/Ride_Videos"
DATE=`date +%Y%m%d`
SRCDIR=`ls -d $SRCDIR/DCIM/*GOPRO`
for file in `ls $SRCDIR/GOPR*.MP4`
do FILENAME=`echo $file|cut -f 6 -d \/|cut -f 1 -d .`
FNAME=`echo $FILENAME|cut -c 6-8`
echo "file '$file'" >> ${SRCDIR}/${FILENAME}.in
for file2 in `ls $SRCDIR/GP*${FNAME}.MP4`
do echo "file '$file2'" >> ${SRCDIR}/${FILENAME}.in
done
cat ${SRCDIR}/${FILENAME}.in
ffmpeg -f concat -safe 0 -i ${SRCDIR}/${FILENAME}.in -c copy ${DESTDIR}/${FILENAME}_${DATE}_all_${SUFFIX}.MP4
for file3 in `cat ${SRCDIR}/${FILENAME}.in|cut -f 2 -d \'`
do rm $file3
done
rm ${SRCDIR}/${FILENAME}.in
done
exit 0
