What is the Shar'i ruling regarding the responsibility of the questioner towards his companion, who suffered material and physical harm in a traffic accident while on the questioner's motorcycle, knowing that they had offered each other rides on their motorcycles, and chose to ride the questioner's motorcycle?

You are not sinful unless you intended [harm] or were negligent. As for compensation for damages, it requires knowing the details of the incident and its circumstances, and identifying the negligent party. The negligent party is liable, and sometimes both parties may share negligence, in which case each guarantees the other. Traffic accidents are subject to the rulings of accidental felonies, and the driver is responsible for any damage he causes, unless the accident was due to an act of God, the action of the injured party, or the fault of a third party. If the driver and the injured party both contributed to causing the damage, then each bears the responsibility for what was lost by the other. Determining liability or innocence requires knowing the details of the accident and the reports of the competent authorities, and the Sharia court is the one that makes decisions in disputes.