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I would think torque would have to be opposite the twist.
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You're right. Think of the action of the system if the bullet is fixed - the barrel must rotate in the opposite direction of the bullet's rotation.
Sort of like a bolt and a nut. The wrench exerts a clockwise torque on the bolt while the nut exerts a counterclockwise torque. When the bolt is snugged up, the torques balance out.
I still have nightmares about Statics and Dynamics.