What is the axis of rotation for a freely moving rigid body after a collision?

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In a collision involving a freely moving rigid body at rest, the axis of rotation can be determined using conservation of angular momentum. When another body collides and sticks to it, the initial angular momentum can be calculated as the cross product of the position vector and the momentum of the colliding body. The final angular momentum remains constant, allowing for the use of the moment of inertia tensor to relate angular momentum to angular velocity. The axis of rotation is not fixed and can change over time, depending on the relationship between angular momentum and angular velocity. Understanding these principles is crucial for analyzing the motion of complex shapes post-collision.
hamidjan
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hi.
I have an essential question. Suppose we have an complex shape at complete rest freely in space. There exist no forces at all. If we collide it in a point, at which axis it will be rotate? How I find it?
I want the answer be in general and for all shapes.
 
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In general, it is complicated.
Both momentum and angular momentum are conserved, but the rotation axis of the object can change in time.
 
welcome to pf!

hi hamidjan! welcome to pf! :smile:

let's keep it simple by assuming that the other body sticks to it after the collision

then you use conservation of angular momentum about its centre of mass …

the initial angular momentum will be r x mv of the other body

the final angular momentum will be the same

now use the moment of inertia tensor to convert the angular momentum vector to the angular velocity vector

(surprisingly, they're not parallel unless the angular momentum is along a principal axis: otherwise, the angular velocity vector rotates about the angular momentum vector)

the (variable) axis of rotation, of course, is along the angular velocity vector :wink:​
 

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