I would like to use my artificial sweetener Equal to make yeast rolls. Will the yeast activate? I've never tried anything like this before. I would like to know before I invest in the time, effort and waste of ingredients.
No. Yeast cannot use Equal (aspartame) to gain caloric energy any more than you can.
How much sugar is your recipe calling for to activate the yeast? The calories in a teaspoon of sugar are insignificant compared to those in the rest of the ingredients, especially after the yeast has consumed some of them.
The yeast will work just fine in a dough with artificial sweetener. Sugar is actually inhibiting the yeast, not helping it (that's why you cannot make yeast dough that's too sweet). Simply put the yeast in the dough as usual and work it.
If by "activate" you mean you are making a preferment, you don't have to do it at all, if you are using dry yeast. The type of dry yeast which needed to be activated has not been on the market for decades.
If you are using fresh yeast, or insist on a longer-kept preferment for flavor development, simply leave the sweetener out of the preferment, it is not needed. From there, continue working as usual. Neither sugar nor sweetener is needed.