YES. You must run a good flow of water until the grinding has stopped. In fact, it is a good idea to run cold water down the disposal before grinding food particles and then also after the grinding has stopped as well. This will ensure that the food particles from your dishes are on their way to sewage plant and not clogging your pipes or backing up your dishwasher.
The most important thing to remember about a garbage disposal is that it is designed to work with your plumbing to dispose of food scraps through your drain pipes. If you don't run enough water before and after you turn the garbage disposal on, you will not send the food particles completely through the disks that cut up the food and you will also not send the food all the way out of your drainage pipes.
If food particles get stuck in the disks of your garbage disposer, this will cause the motor to stop working and will probably throw of the power. The first thing to do in this case is to press the red restart button on the disposer. If you hear a humming, but not the motor moving, you may have to take a few steps to get your garbage disposal working again.
Only Attempt This Step With The Disposer Unplugged. There should be a Allen wrench or some type of hexagonal wrench that came with your garbage disposal. In order to free the blades, you will have to use this wrench to manually turn the blades to free them of food particles. Once this is accomplished, plug the disposer in and make sure to run plenty of cold water to make sure any remaining food particles are removed.
However, the best way to avoid problems with your garbage disposal in the first place is to make sure that the food particles you put down it are small and that you run plenty of cold water down the drain before and after you use it.