Some (many? most?) asteroids contain some water and carbon. Proposals exist to use water as a propellant, either directly by electrically heating it so that it turns into steam which is the reaction mass, or by chemically turning water and optionally the carbon into propellants, for example methane and oxygen, which in turn can be used to fuel conventional rocket drives.

In fact, the chemical reaction path is lossy: The two main advantages of producing chemical rocket fuel first instead of using water directly as reaction mass are (1) the re-use of existing engines and (2) the high energy density of the fuel which allows higher-powered rocket motors. If the expedition to the asteroid can bring water powered engines like this one and is happy with the comparatively low output, direct water use is probably more efficient. One the other hand, if we imagine a manned expedition the ability to produce rocket fuel and oxygen through electrolysis is probably necessary and present in any case, so stopping the asteroid's rotation with conventional rocket motors would only use existing resources.

As an aside: If you are interested in large-scale scenarios that imagine asteroids as resources I recommend reading Neal Stephenson's Seveneves.

Some (many? most?) asteroids contain some water and carbon. Proposals exist to use water as a propellant, either directly by electrically heating it so that it turns into steam which is the reaction mass, or by chemically turning water and optionally the carbon into propellants, for example methane and oxygen, which in turn can be used to fuel conventional rocket drives.

In fact, the chemical reaction path is lossy: The two main advantages of producing chemical rocket fuel first instead of using water directly as reaction mass are (1) the re-use of existing engines and (2) the high energy density of the fuel which allows higher-powered rocket motors. If the expedition to the asteroid can bring water powered engines like this one and is happy with the comparatively low output, direct water use is probably more efficient. One the other hand, for a manned expedition the ability to produce rocket fuel and oxygen through electrolysis is probably necessary and present in any case, so stopping the asteroid's rotation with conventional rocket motors would only use existing resources.

As an aside: If you are interested in large-scale scenarios that imagine asteroids as resources I recommend reading Neal Stephenson's Seveneves.

Some (many? most?) asteroids contain some water and carbon. Proposals exist to turn them into propellants, for example methane and oxygen, which in turn can be used to fuel rocket drives.

As an aside: If you are interested in ideas for using asteroids as resources I recommend reading Neal Stephenson's Seveneves.

Some (many? most?) asteroids contain some water and carbon. Proposals exist to use water as a propellant, either directly by electrically heating it so that it turns into steam which is the reaction mass, or by chemically turning water and optionally the carbon into propellants, for example methane and oxygen, which in turn can be used to fuel conventional rocket drives.

In fact, the chemical reaction path is lossy: The two main advantages of producing chemical rocket fuel first instead of using water directly as reaction mass are (1) the re-use of existing engines and (2) the high energy density of the fuel which allows higher-powered rocket motors. If the expedition to the asteroid can bring water powered engines like this one and is happy with the comparatively low output, direct water use is probably more efficient. One the other hand, if we imagine a manned expedition the ability to produce rocket fuel and oxygen through electrolysis is probably necessary and present in any case, so stopping the asteroid's rotation with conventional rocket motors would only use existing resources.

As an aside: If you are interested in large-scale scenarios that imagine asteroids as resources I recommend reading Neal Stephenson's Seveneves.