Your first task should be to collect some data from the dumbbell. There are many, many different schemes that could be used to classify the data, but until you have some sample data to work with, it is hard to predict exactly what will work best.

If you get 5 different people to do all of the exercises and look at the resulting data yourself (e.g. pilot the different parts of the data collected), can you distinguish which exercise is which? This may give you hints on what pre-processing you might want to perform on the data before sending it to a classifier.

First you create a large training set. Then you train it, telling it what actually happens.

And you might uses averages of data as well. Perhaps use actual movement and movement that is averaged over 2 sec 5 sec and 10 sec. use those too as for input nodes.

while exercising the trained network can be feeded with the averaged data as well ea (the last x samples divided by x), this will give you a stable approach. Otherwise the neural network can become hectic erratic.

Notice the training set might require averaged data as well and thus you will need a large training set.