Final answer:
The decision to allow a goalkeeper to retrieve a new glove during a game would depend on the specific rules of the ice hockey league. In a physics context, the scenario may be used to illustrate principles such as conservation of momentum and Newton's Third Law rather than focusing on sports regulations.
Step-by-step explanation:
To determine if the goalkeeper should be allowed to go to their players' bench to obtain a new catching glove and remain on the ice for the ensuing face-off, one would need to consult the specific rules of the ice hockey league in question. Typically, equipment repair or replacement is handled with certain time constraints in mind to keep the game flowing and fair.
However, in the context of the provided information which includes various examples of physics in motion like the frictionless ice surface, the question seems to be using the scenario of the goalkeeper as an illustration for a physics concept rather than a regulations query. In a physics context, such as an ice hockey goalie catching a hockey puck and recoiling in an inelastic collision, the focus would be on the conservation of momentum and energy rather than the rules of the sport.
If this is a conceptual physics question, it would be more fitting to discuss phenomena such as the action-reaction principle as demonstrated when an ice hockey player must shoot backward to give the puck velocity towards the goal on a frictionless ice surface. These illustrate the principles of Newton's Third Law of Motion and conservation of momentum.