Capturing images on fast moving conveyor belt This may or may not be an image processing problem. 
I am developing a simple system that captures images of a part as they are being manufactured and sent out along the conveyor belt. 

I've solved the alignment problems, and background subtraction problem that this application requires. Everything is working in my prototype setup where I manually place parts with and without defect under the camera in different lighting conditions, position and other realistic variables. My setup uses Logitech C920 web cam, the software is able to process each frame in less than 1 second on average. 

The problem arises when I start simulating the parts on the moving conveyor belt, it is unable to capture frame fast enough resulting in motion blur.

How is the issue approached in this industry? 
If I switch to use a DSLR and use the correct f-stop (etc.) will that solve the blur problem? If so, wouldn't DSLR overheat since it has to capture so many frames for hours and hours and hours? 

PS: speed of conveyor belt is fast but slow enough to easily track with human eyes. I don't have the information about the exact speed at this time.
Try reducing exposure time if your camera allows that. With the short exposure time the conveyor belt should be well-lit.

If that is not enough, a common solution is to use a flash which is synchronized to the camera. If a sync signal is not readily available from the camera and you can't trigger the camera with your own sync signal, you probably could find a pin on your prototype camera's circuit board that carries a signal you can sync the strobe light to.

Without synchronization, setting the strobe rate to about 2/3 of the frame rate may be a reliable solution that gives good frames separated by at most one bad frame. Whether that works depends on whether there is a rolling or a progressive shutter and on the exposure time. Other ratios closer to 1 might work better in case of a rolling shutter and/or a short exposure time.

About DSLR cameras, you should use a camera that uses an electronic shutter in the mode (still/video) you would use. Cameras do not normally overheat but a mechanical shutter is only specified for that many cycles.

Also line scanners are a possibility, but I have no idea if those are commonly used. Think of a flatbed scanner where instead of moving the scanner head the target is moving. Those never blur the image but require bright illumination along the line being imaged. That may be easier to arrange than illumination over a large area, but it's a more exotic solution than a normal area camera.

More of an anecdote: A synchronously rotating prism with parallel opposite sides, located in front of the camera, can approximately compensate for linear motion.