How do I add an impulse rotation that rotates the object along the direction thrown

To achieve a rotation you need to apply an angular impulse not a (linear) impulse. The actor you apply the angular impulse to needs to be simulating physics in order to react properly to it. Secondly, a rotation impulse is applied “around” a rotational axis. In the case of your axe, you want to apply it around its right vector so it rotates on a plane which contains its trajectory.

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