# Which axis rigid body rotate?

1. Apr 16, 2013

### hamidjan

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.

2. Apr 16, 2013

### Staff: Mentor

In general, it is complicated.
Both momentum and angular momentum are conserved, but the rotation axis of the object can change in time.

3. Apr 16, 2013

### tiny-tim

welcome to pf!

hi hamidjan! welcome to pf!

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