We DON’T want Mashiach, the righteous children of sinners, calculating when Mashiach will come, the rabbi who didn’t believe in Mashiach
Although there is a prohibition of Muktzeh for items that are newly created on Shabbos, rainwater does not fall under this category. The reason for this is that rainwater is not newly created, only that it now has fallen from the clouds. It is not Muktzeh provided that it is fit for some use.
Review: If the part that broke is not fit for use and one plans on throwing it out, or even if it is fit for use, but most people throw it out, it is Muktzeh.
If the part that broke is fit for use and people are accustomed to keep it, it is not Muktzeh.
Generally, if the part that broke off is not fit for use but it is common to keep so that it can be reattached after Shabbos, it is not Muktzeh.
The above is only if the main part of the utensil can be easily used. If it can be used but it is uncomfortable to use (like broken glasses), one may not us it out of concern that one will fix it.
If the item was attached to the ground (or home) and broke, it cannot be moved on Shabbos.
A door or a door handle that comes off before or on Shabbos is considered Muktzeh and cannot be used. The same is true for anything attached to a structure, such as a window, blinds, and toilet seats.
Glasses that break, if they can be easily reassembled (using a glasses kit), one may not move the glasses or the broken parts, because there is a concern that one may come to do so. (This is different than the Halacha before as here the item can still be used but it is uncomfortable and therefore there is more of a concern of fixin
A utensil that broke is usually considered Muktzeh as it serves no purpose.
However, in certain circumstances, if something breaks in a way that the broken parts can be put back together at a later point, it is not Muktzeh. It would have to be something in which the primary part of the item can be used.
For example, a button that falls off on Shabbos may be moved as it will be sewn back on after Shabbos. Similarly, if the arm rest of a chair falls off, one may move the arm rest on Shabbos.