Is it a good idea to install a motion detector instead of multiple contact sensors for each window in a room that has 4 large windows ?
Yes, Motion Sensors can cover a broad area, like if someone enters through the window. Remember to avoid pointing the sensor directly at the window (sunlight can potentially cause triggering of a false alarm). Generally, it is good to mount the motion sensor in the corner of the same wall of the windows.
One disadvantage of using Motion Sensors instead of Contact Sensors is that in the “HOME” alarm mode, many people have set their motion sensors to not activate the Alarm Base Station siren because they are still at home inside. This way, you can roam about freely inside without worrying about triggering a Motion Sensor. Using Contact Sensors would allow you to form a “protective barrier” while you are still inside in the “Home” alarm mode. Using only Motion sensors would leave those windows unprotected while you are home and them disabled.
But in the “Away” Alarm mode (when nobody is inside the house) having the Motion Sensors enabled to trigger the alarm is a very effective method to cover windows that do not have Contact sensors installed.
So, it really depends what combination of Motion and Contact sensors would fit your needs the best. For example, I do have my garage Motion Sensor enabled while in the “Home” alarm mode, so even though I can freely roam about in my house, my garage is protected and I am aware that if I accidentally enter the garage with the Home Mode active that I would set off my alarm. I also know of some people that configure their “Home” alarm mode settings so that their downstairs motion sensors are active, while they remain upstairs asleep at night. So, there isn’t a “One solution fits all” answer for your question.